PUBLICATIONS:

__Books__

- M.A. Golberg
and C.S. Chen,
*Discrete Projection Methods for Integral Equations*, Computational Mechanics PublicationsSouthampton, Boston*,**,*1997 (425 pages). - (Editors)
C.S. Chen, C.A. Brebbia
and D. Pepper,
*Boundary Element Technology XIII*, WIT PRESS, June, 1999. - (Editors)
C.S. Chen, A. Karageorghis,
Y.S. Smyrlis, The Method of Fundamental
Solutions - A Meshless
Method, Dynamic Publishers, 2008.
- C.S. Chen,
Y.C. Hon, R.S. Schaback,
Scientific Computing with Radial Basis Functions,
under review.
- Wen Chen, Zhuo-Jia
Fu, C.S. Chen, Recent advances on radial basis function collocation
methods,
2014, Springer.

__Book
Chapters__

- M.A. Golberg
and C.S. Chen, The method of fundamental solutions for potential,
Helmholtz and
diffusion problems, in
*Boundary Integral Methods - Numerical and Mathematical Aspects*, ed. M.A. Golberg, Computational Mechanics Publications, 1998, pp.103-176. - C.S.
Chen, M.A. Golberg,
R.S. Schaback,
Recent developments of the dual reciprocity method using compactly
supported
radial basis functions, in:
*Transformation of Domain Effects to the Boundary*, ed. Y.F. Rashed, WIT PRESS, pp183-225, 2003. - C.S.
Chen, C.M. Fan, J. Monroe, The method of fundamental solutions for
solving
elliptic partial differential equations with variable coefficients, in
The
Method of Fundamental Solutions - A Meshless
Method,
eds. C.S. Chen, A. Karageorghis,
Y.S. Smyrlis, Dynamic
Publishers, p. 75-105, 2008.
- P.H.
Wen, C.S. Chen, Y.W. Liu, Shear deformable plate analysis by the method
of
fundamental solutions: static and dynamic cases, in The Method of
Fundamental
Solutions - A Meshless
Method, eds. C.S. Chen, A. Karageorghis,
Y.S. Smyrlis,
Dynamic Publishers, p. 227-246, 2008.

- C.Y. Chan
and C.S. Chen, A numerical method for semilinear
singular parabolic quenching problems,
*Quarterly of Applied Mathematics*, 47, pp 45-57, 1989. - C.Y. Chan
and C.S. Chen, Critical length for global existence of solutions for
coupled semilinear
singular parabolic problems,
*Quarterly Applied Mathematics***,**47, pp 661-671, 1989. - D. Wan,
Peter Shiue and C.S.
Chen, Value set of polynomial over finite fields,
*Proceedings of American Mathematical Society*, Vol. 119, No. 3, pp 711 - 717, 1993. - M. Golberg and C. S. Chen, On a
method of Atkinson for evaluating domain integrals in the boundary
element method,
*Applied Mathematics and Computation***,**60, 1994, pp125-138. - C. S. Chen
and A. Muleshkov,
Critical lengths for some nonlinear differential equations,
*Dynamic Systems and Applications*, 3, 1994, pp121-134. - M. Golberg and C.S. Chen, The
theory of radial basis functions applied to the BEM for inhomogeneous
partial differential equations,
*Boundary Elements Communications***,**5, pp 57-61, 1994. - C.S. Chen,
The method of fundamental solution for nonlinear thermal explosion,
*Communications in Numerical Methods in Engineering,*11, pp. 675-681, 1995. - C.S. Chen,
The method of fundamental solutions and quasi-monte
carlo
methods for Possion
equation,
*Lecture Notes in Statistics*106, pp. 158-167, 1995.**,** - M.A. Golberg, C.S. Chen and S.R. Karur, Improve multiquadric interpolation for
partial differential equations,
*Engineering Analysis with Boundary Elements*, 18, 9-17, 1996. - M.A. Golberg and C.S. Chen, A
bibliography on radial basis function approximation,
*Boundary Elements Communications*, 7 (4), 155-163, 1996. - M.A. Golberg , C.S. Chen, H. Bowman and H.
Power, Some comments on the radial basis functions in the dual
reciprocity method,
*Computational Mechanics,*21, 141-148**,**1998. - C.S. Chen
and Y.F. Rashed,
Evaluation of thin plate spline based particular solution for
Helmholtz-type operators for the DRM,
*Mechanics Research Communications*, 25(2), 1998, 195-201. - M. Zerroukat, H. Power and C.S.
Chen, A numerical method for heat transfer problem using collocation
and radial basis functions,
*International Journal of Numerical Methods in Engineering*42, pp. 1263-1278, 1998.__,__ - C.S. Chen,
M.A. Golberg and Y.C.
Hon, Numerical justification of the method of fundamental solutions and
the quasi-Monte Carlo method for Poisson-type equations,
*Engineering Analysis with Boundary Elements*, 22, pp. 61-69, 1998. - C.S. Chen,
M.A. Golberg and Y.F. Rashed, A mesh free method for
linear diffusion equations,
*Numerical Heat Transfer, Part B,*33, 1998, 469-486. - C.S. Chen,
M.A. Golberg and Y.C.
Hon, The method of fundamental solutions and quasi-Monte Carlo method
for diffusion equations,
*International Journal of Numerical Methods in Engineering*, 43, 1421-1436, 1998. - M.A. Golberg, C.S. Chen and Y.F. Rashed, The annihilator method
for computing particular
solutions to partial differential equations, to appear in
*Engineering Analysis with Boundary Elements*, 23, 275-279, 1999. - C.S. Chen,
C.A. Brebbia and H.
Power, Dual reciprocity method using compactly supported radial basis
functions,
*Communications in Numerical Methods in Engineering*15, 137-150__,__**,**1999. - M.A. Golberg, C.S. Chen and H.
Bowman, Some recent results and proposals for the use of radial basis
functions in the BEM,
*Engineering Analysis with Boundary Elements*, 23, 285-296**,**1999. - A.S. Muleshkov, M.A. Golberg and C.S. Chen,
Particular solutions of Helmholtz-type operators using higher order polyharmonic splines,
*Computational Mechanics*, 24, 411-419, 1999. - M.A. Golberg, C.S. Chen and M.
Ganesh, Particular solutions of the 3D modified Helmholtz-type
equations using compactly supported radial basis functions,
*Journal of**Engineering Analysis with Boundary Elements*, vol. 24, pp. 539-547, 2000. - M. Marcozzi, S. Choi and C.S. Chen,
On the use of boundary conditions for variational
formulations arising in financial mathematics,
*Journal of Applied Mathematics and Computation,*Vol. 124, pp. 197-214, 2001. - M.A. Golberg, C.S. Chen , A mesh free
method for solving nonlinear reaction-diffusion equations, the
*Journal of Computer Modeling in Engineering & Science*, 2, pp. 87-96, 2001. - A. D.-H.
Cheng, C.S. Chen, M.A. Golberg
and Y.F. Rashed, BEM
for thermoelasticity
and elassticity with
body force - a revisit,
*Engineering Analysis with Boundary Elements*, Vol. 25, pp. 377-387, 2001. - Y.F. Rashed, C.S. Chen and M.A. Golberg, Efficient evaluation of
plate-half space interaction using contour integrals,
*Applied Mathematics Modeling*, Vol. 25, pp. 967-978, 2001. - Jichun Li and C.S.
Chen, A Simple efficient algorithm for interpolation between different
grids in both 2D and 3D,
*Mathematics and Computers in Simulation*, Vol. 58(2), pp. 125-132, 2001 - C.S.
Chen, M.A. Golberg, M. Ganesh, A. H-D. Cheng,
Multilevel compact radial functions based computational schemes for some elliptic problems,
*Journal of Computers and Mathematics with Application*, 43, pp. 359-378, 2002 - Xin Li, C.H. Ho
and C.S. Chen, Computational test of approximation of functions and
their derivatives by radial basis functions,
*Neural and Parallel in Scientific Computing*, 10, pp. 25-46, 2002. - Jichun Li, Y.C.
Hon and C.S. Chen, Numerical comparisons of two meshless
methods using radial basis functions,
*Engineering Analysis with Boundary Elements*, 26, pp. 205-225, 2002. - M.A. Golberg, A.S. Muleshkov, C.S. Chen, A D.-H.
Cheng, Polynomial particular solutions for some partial differential
operators,
*Numerical Methods for Partial Differential Equations*, 19, pp. 112-133, 2003. - Jichun Li, A.
D.-H. Cheng and C.S. Chen, On
the efficiency and exponential convergence of multiquadric
collocation methods compared with finite element method,
*Eng. Anal. with Boundary Elements*, 27, pp. 251-257, 2003. - C.S. Chen,
G. Kuhn, Jichun Li and
G. Mishuris, Radial
basis functions for solving near-singular Poisson's Problems,
*Communication in Numerical Methods in Engineering*, 19, pp. 333-347, 2003 - Jichun Li and C.S.
Chen, Some observations on unsymmetric
radial basis functions collocation methods,
*International Journal of Numerical Methods in Engineering*, 57, pp. 1085-1094, 2003 - B. Sarler, Janez
Perko, C.S. Chen,
Radial basis function collocation method solution of natural convection
in porous media,
*International Journal of Numerical Methods for Heat and Fluid Flow,*14(2), pp. 187-212, 2004. - X. Li, C.S.
Chen, A mesh free method using Hyperinterpolation
and Fast Fourier Transform for solving differential equations,
*Engineering Analysis with Boundary Elements*, 28, pp. 1253-1260, 2004. - M.S. Ingber, C.S. Chen, and J.A. Tanski,
A Mesh free approach using radial basis functions and parallel domain
decomposition for solving three dimensional diffusion equations,
*International Journal of Numerical Methods in Engineering,*60, pp. 2183-2201, 2004. - C.S.
Chen, A.S. Muleshkov,
M.A. Golberg, R.M.M. Mattheij, A
mesh free approach to solving the axi-symmetric
Poisson's equation,
*Numerical Methods for Partial Differential Equations*, 21, pp. 349-367, 2005. - C.J.S. Alves, C.S. Chen, Approximating
functions and solutions of non
homogeneous partial differential equations using the
method of fundamental solutions,
*Advances in Computational Mathematics,*23, pp. 125-142, 2005. - A.S. Muleshkov, M.A. Golberg, C.S. Chen, Particular
solutions for axisymmetric Helmholtz-type operators,
*Engineering Analysis with Boundary Elements*, 29, pp. 1066-1076, 2005. - D. L. Young
, T. K. Wong , C. W. Chen , C.M. Fan , C.S. Chen, Solution of
Maxwell's equations by meshless
time domain method, CMC, 2, pp. 267-276, 2005
- H.A. Cho, C.
S. Chen, and M.A. Golberg,
Some comments on mitigating the ill-conditioning of the method of
fundamental solutions,
*Engineering Analysis with Boundary Elements*, 30, pp. 405-410, 2006. - S.Y. Reutskiy and C.S. Chen,
Approximation of multivariate functions and evaluation of particular
Solutions using Chebyshev
Polynomial and Trigonometric Basis Functions,
*International Journal in numerical methods in engineering*, 67, pp. 1811-1829, 2006. - D. L. Young
, C.C. Tsai, Y.C. Lin, C.S. Chen, The Method of Fundamental Solutions
for Plate Vibrations,
*CMC*, 4, 1-10, 2006. - C.-S. Huang,
S. Wang, C.S. Chen, and Z.-C. Li, A
Radial Basis Collocation Method for Hamilton-Jacobi-Bellman Equations,
*Automatica*, 42, 2201-2207, 2006. - Andreas Karageorghis, C.S. Chen, and Y-S
Smyrlis, A matrix
decomposition method for solving large scale problems using radial
basis functions - approximation of functions and their derivatives,
*Applied Numerical Mathematics*, 57, 304-319, 2007. - Radovan Gospavic, Viktor Popov, Milesa Sreckovic,
C.S. Chen, DRM-MD approach for modeling laser-material interaction with axial
symmetry,
*Engineering Analysis with Boundary Elements*, 31, 200-208, 2007. - C.S. Chen, Sungwook Lee, C.-S. Huang, Derivation of particular solution using chebyshev polynomial based
functions
*, International Journal of Computational Methods*, Vol. 4, No. 1, 15-32, 2007. - E.V. Glushkov, N.V. Glushkova, C.S. Chen, Semi-analytical solution to heat-transfer problems
using Fourier transform technique, radial basis functions and the
method of fundamental solutions,
*Numerical Heat Transfer, Part B*, 52 (5), 409-427, 2007. - Jiu Ding and
C.S. Chen, Particular solutions of some elliptic partial differential
equations via recursive formulas,
*Journal of University of Science and Technology of China*, 37(11), 1338-1347, 2007. - Sergiy Reutskiy, C.S. Chen, Haiyan Tian,
A boundary meshless
method using Chebyshev
interpolation and trigonometric basis function for solving heat
conduction problems,
*International Journal Numerical Methods in Engineering*, 74, 1621-1644, 2008. - Haiyan Tian, Sergiy
Reutskiy, C.S. Chen,
A basis function for approximation and the solution of partial
differential equations,
*Numerical Methods for Partial Differential Equations*, 24, 1018-1036, 2008. - J. Ding,
H.Y. Tian, C.S. Chen,
The recursive formulation of particular solutions for some elliptic
PDEs with polynomial source functions
*, Communication in Computational Physics*, 5, 942-958, 2009. - C.C. Tsai,
A. H.-D. Cheng, C.S. Chen, Particular solution of splines and monomials
for polyharmonic and
products of Helmhlotz
operators,
*Engineering Analysis with Boundary Elements,*33, 514-521, 2009. - C.C. Tsai,
C.S. Chen, T.W. Hsu, The method of particular solutions for solving
axisymmetric polyharmonic
and poly-Helmholtz equations, Engineering Analysis with Boundary
Elements, 33, 1396-1402, 2009.
- C.M. Fan,
C.S. Chen, J. Monroe, The Method of fundamental Solutions for solving
convection-diffusion equations with variable coefficients,
*Advances in Applied Mathematics and Mechanics*, 1, 215-230, 2009. - C.S. Chen,
S.Y. Reutskiy, V.Y. Rozov,
**The method of the fundamental solutions and its modifications for electromagnetic field problems,***Computer Assisted Mechanics and Engineering Sciences,*16, 21-33, 2009. - A. Karageorghis, C.S. Chen, and
Y.--S. Smyrlis, Matrix
decomposition RBF algorithm for solving 3D elliptic problems,
*Engineering Analysis with Boundary Elements*, 33, 1368-1373, 2009. - C.C. Tsai,
C.S. Chen, Tai-Wen Hsu, The method of particular solutions for solving
axisymmetric polyharmonic
and poly-Helmholtz equation,
*Engineering Analysis with Boundary Elements*, 33, 1396-1402, 2009. - Guangming
Yao, C.S. Chen, C.C. Tsai, A Revisit on the derivation of the
particular solution for the differential
operator \Delta^{2} - \lambda^{2},
*Advances in Applied Mathematics and Mechanics*,*1, pp. 750-768, 2009.* - Ting On Kwok, Leevan
Ling, C.S. Chen, Solving 3D inhomogeneous elliptic equations adaptively
with the method of particular solutions, International Journal of
Computational Methods, 7,
499-511, 2010.
- P.H.
Wen, C.S. Chen, The method of particular solutions for solving scalar
wave equations, International Journal for Numerical Methods in
Biomedical Engineering, 26, 1878-1889, 2010.
- Ming
Li, C.S.
Chen, C.H. Tsai, Meshless
method based on radial basis functions for solving parabolic partial
differential equations with variable coefficients , Numerical
Heat Transfer Part B：Fundamentals,
2010; 57: 333-347.
- Ming Li,
Y.C. Hon, C.S. Chen, A meshless
method for solving nonhomogeneous Cauchy Problems,
Engineering Analysis with Boundary Elements, 35, 499-506, 2011.
- Guangming Yao, C.S.
Chen, Bozida Sarler, A comparison of three
explicit local meshless
methods using Radial Basis Functions, Engineering Analysis with
Boundary Elements, 35, 600-609, 2011.
- C.S. Chen,
C.M. Fan, P.H. Wen, The method of particular solutions for solving
elliptic problems with variable coefficients, International Journal of
Computational Methods, 8, 545-559, 2011.
- Guangming Yao, C.S.
Chen, Joseph Kolibal, A
localized approach for the method of approximate particular solutions, Computers
and Mathematics with Applications, 61,
2376-2387, 2011.
- A. Tadeu, C.S. Chen, J. Antonio, Nuno Simoes,
A boundary meshless
method for solving heat transfer problems using Fourier transform,
Advances in Applied Mathematics and Mechanics, 3, 572-585, 2011.
- C.S. Chen,
C.M. Fan, P.H. Wen, The method of particular solutions for solving
certain partial differential equations, Numerical Methods for Partial
Differential Equations, 28,
506-522, 2012.
- Tongsong Jiang, Ming
Li, and C.S. Chen, The method of particular solutions for solving
inverse problems of a nonhomogeneous convection-diffusion equation with
variable coefficients, Numerical Heat Transfer, Part A, 61, 338-352,
2012.
- Wen Chen, Ji Lin, C.S. Chen, The method of
fundamental solutions for solving exterior axisymmetric Helmholtz
problems with high wave number, Advances in Applied Mathematics and
Mechanics, 5(4), 477-493, 2013.
- C.S.
Chen, C-S. Huang, K.H. Lin, On the convergence of the MFS-MPS Scheme
for 1D Poisson's Equation, International Journal of Computational
Methods, 10(2), 2013. DOI:
10.1142/S0219876213410065
- Xingrong Jiang, Wen Chen, C.S. Chen, A fast method of fundamental solutions for solving Helmholtz-type equations, International Journal of Computational Methods, 10(2), 2013. DOI: 10.1142/S0219876213410089.
- Ming Li, Wen Chen, C.S. Chen, A localized RBFs collocation method for solving high dimensional PDEs, Engineering Analysis with Boundary Elements, 37, 1300-1304, 2013.
- Xinrong Jiang, Wen Chen, C.S. Chen, Fast multipole accelerated boundary knot method for inhomogeneous Helmholtz problems, Engineering Analysis with Boundary Elements, 37, 1239-1243, 2013.
- Ming Li, C.S. Chen, A. Karageorghis, The MFS for the solution of harmonic boundary value problems with non-harmonic boundary conditions, Computers with Mathematics with Applications, 66, 2400-2424, 2013.
- Ji Lin, W. Chen, C.S. Chen, X.R. Jiang, Fast boundary knot method for solving axisymmetric Helmholtz problems with high wave number, CMES, 94(6), 485-505, 2013.
- Ji
Lin,
Wen Chen, CS Chen, XR Jiang, Fast boundary knot method for solving
axisymmetric
Helmholtz problems with high wave-number,
*CMES: Computer Modeling in Engineering & Sciences*, 94( 6), 485-505, 2013.

- C.Y.
Lin, M.H. Gu, D.L.
Young, C.S. Chen, Localized Method of approximate particular solutions
with Cole-Hopf
transformation for multi-dimensional Burgers equations, Engineering
Analysis with Boundary Elements, 40, 78-92, 2014.
- Ming Li, C.C. Chu, D.L. Young, C.S. Chen, Transient 3D heat conduction in functionally graded materials by the method of fundamental solution, Engineering Analysis with Boundary Elements, 45, 62-67, 2014.
- G. Feng, Ming Li, C.S. Chen, On the ill-conditioning of the method of fundamental solutions for non-harmonic boundary data, Engineering Analysis with Boundary Elements, 41, 98-102, 2014.
- Ji Lin, Wen Chen, C.S. Chen, Numerical treatment of acoustic problems with boundary singularities by singular boundary method, Journal of Sound and Vibration, 333, 3177-3188, 2014.
- Ming Li, Ghizlane Amazzar, Ahmed Naji, C.S. Chen, Solving Biharmonic equation using the localized method of approximate particular solutions, International Journal of Computer Mathematics, 91(8), 1790-1801, 2014.
- Xiao-Yan Liu, Wen Li, Ming Li, C.S. Chen, Circulant matrix and conformal mapping for solving partial differential equations, Computers and Mathematics with Applications, 68(3), 67-76,2014.
- J. Sladek, V. Sladek, S. Krahulec, C.S. Chen, D.L. Young, Analyses of circular magnetoelectroelastic plates with functionally graded material properties, Mechanics of Advanced Materials and Structures, 22, 479-489, 2015.
- Wen Li, Ming Li, C.S. Chen, Compactly supported radial basis functions for solving certain high order partial differential equations in 3D, Engineering Analysis with Boundary Elements, 55, 2-9, 2015.
- Ji Lin, Wen Chen, C.S. Chen, A new scheme for the solution of reaction diffusion and wave propagation problems, Applied Mathematical Modelling, 38, 5651-5664, 2015.
- C.S. Chen, Xingrong Jiang, Wen Chen, Fast solution of the modified Helmholtz equation with the method of fundamental solutions, Communications in Computational Physics, 17(3), 867-886, 2015.
- A.R.
Lamichhane, C.S. Chen, The close-form particular solutions for Laplace
and biharmonic operators using Gaussian radial basis functions, Applied
Mathematics Letters, 46, 50-56, 2015.
- Xueying Zhang, C.S. Chen, Local RBFs based collocation methods for unsteady Navier-Stokes equations, Advances in Applied Mathematics and Mechanics, 7, 430-440, 2015.
- M. Li, C.S. Chen, Y.C. Hon, P.H. Wen, Finite integration method for two-dimensional partial differential equations, Applied Mathematical Modelling, 39, 4979-4994, 2015.
- G. Yao, Jia Duo, C.S. Chen, L.H. Shen, Implicit local radial basis function interpolations based on function values, Applied Mathematics and Computation, 265,91-102,2015.
- C.S. Chen, Guangming Yao, D.L. Young, An improved localized method of approximate particular solutions for solving near singular problems, Computers with Mathematics with Applications, 70, 2883-2894, 2015.
- Xiao-Yan Liu, A. Karageorghis, C.S. Chen, A Kansa-radial basis function method for elliptic boundary value problems in annular domains, Journal of Scientific Computing, 65, 1240-1269, 2015.
- Xueing Zhang, Muyuan Chen, C.S. Chen, Zhiyong Li, Local method of approximate particular solutions for solving unsteady Navier-Stokes problem, Applied Mathematical Modelling, 40, 2265-2273, 2016.

- Ming Li, Z.L. Tian, Y.C. Hon, C.S. Chen, P.H. Wen, Improved finite integration method for partial differential equations, Engineering Analysis with Boundary Elements, 64,230-236，2016.
- A.R. Lamichhane, D.L. Young, C.S. Chen, Fast method of approximate particular solutions using Chebyshev interpolation, Engineering Analysis with Boundary Elements, 64, 290-294, 2016.
- Ji
Lin, C.S. Chen, C.S. Liu, Fast solution of three-dimensional Helmholtz
equations by the method of fundamental solutions, Communications
in Computational Physics, 20(2), 512-533, 2016.

- C.S. Chen, A. Karageorghis, Yan Li, On choosing the location of the sources in the MFS, Numerical Algorithms, 72, 107-130, 2016.
- A. Karageorghis, C.S. Chen, Xiao-Yan Liu, Kansa-RBF algorithms for elliptic problems in axisymmetric domain, SIAM Scientific Computing, 38-1, A471-A499, 2016.
- A.R. Lamichhane, C.S. Chen, Particular solution of Matern RBFs and its implementation in the method of particular solutions, International Journal of Computers and Mathematics, 94(4), 690-706, 2017.
- Thir Dangal, C.S. Chen, Ji Lin, Polynomial particular solutions for solving elliptic partial differential equations, Computers and Mathematics with Applications, 73(1), 60-70, 2017.
- Xiaoyan Liu, C.S. Chen, Andreas Karageorghis, Conformal mapping for the efficient solution of Poisson problems with the Kansa-RBF method, Journal of Scientific Computing, 71(3), 1035-1061, 2017.
- Thir Dangal, C.S. Chen, The method of particular solutions for finding the critical domains for the quenching problems, Neural, Parallel, and Scientific Computing, 25, 135-148, 2017.
- Zhaolu
Tian, Zi-Cai Li, Hung-Tsai, C.S. Chen, The method of fundamental solutions for
the modified Helmholtz equation, Applied Mathematics and Computation, 305, 262-281, 2017.
- Xiangnan Pei, C.S. Chen, Fangfang Dou, The MFS and MAFS for solving Laplace and biharmonic equations, Engineering Analysis with Boundary Element, 80, 87-93, 2017.
- Hui Lv, Fang Hao, C.S. Chen, The MFS versus the Trefftz method for the Laplace equation in 3D, Engineering Analysis with Boundary Elements, 83, 133-140, 2017.
- Andreas Karageorghis, M.A. Jankowska, C.S.
Chen, Kansa RBF algorithm for elliptic problems in
regular polygonal domain, Numerical Algorithm, 79, 399-421, 2018.

- Ji Lin, C.S. Chen, Fajie Wang, Thir Dangal, A new backward node interpolation method using polynomial basis functions for plane bending vibrations, Applied Mathematical Modeling, 49, 452-469, 2017.
- Ji Lin, C.S. Chen, Fajie Wang, Thir Dangal, Method of particular solutions using polynomial basis functions for the simulation of plate bending vibrations problems, Applied Mathematical Modelling, 49,452-469, 2017.
- M. Jankowska, A. Karageorghis, and C.S. Chen, Kansa RBF method for nonlinear problems, Int. J. comp. Meth. and Exp. Meas., 6(6), 1-8, 2018.
- Zhao-Lou
Tian, Xingxinang Li, Chia-Ming Fan, C.S. Chen, The method of particular
solutions using trigonometric basis functions, Journal of
Computational and Applied Mathematics, 335, 20-32, 2018.

- M.
Jankowska, A. Karageorghis, and C.S. Chen, improved Kansa RBF method
for the solution of nonlinear boundary value problems, Engineering Analysis
with Boundary Elements， 87， 173-183, 2018.

- Jingang Xiong, Pengfei Jiang, Hui Zheng, C.S. Chen, A high accurate simulation of thin plate
problems by using the method of approximate particular solutions with high
order polynomial basis, Engineering Analysis with Boundary Elements, 94,
15-158, 2018.

- Ji Lin, A.R. Lamichhane, C.S. Chen, Jun Lu, The adaptive source selection algorithm of the method of fundamental solutions for the solution of harmonic boundary value problems with non-harmonic boundary conditions, Engineering Analysis with Boundary Elements, 95, 154-159, 2018.
- Xiao-yan Liu, C.S. Chen, Wen Li, Ming Li, Particular solutions of products of Helmholtz-type equations using the Matern function, Computers and Mathematics with Applications, 75, 3158-3171, 2018.
- Wanru Chang, C.S. Chen, Wen Li, Solving fourth order differential equations using particular solutions of Helmholtz-type equations, American Mathematics Letters, 86, 179-185, 2018.
- Fangfang Dou, Zi-Cai Li, C.S. Chen, Zhaolu Tian, Analysis on the method of fundamental solutions for biharmonic equations, Applied Mathematics and Computation, 339, 346-366, 2018.
- T.C. Wang, L.H. Shen, D.L. Young, C.S. Chen, Local RBF-DQ method for MHD duct flows at high Hartmann numbers, MOJ Applied Bionics and Biomechanics, 2(1), 71-82, 2018.
- Fangfang Dou, Yanshan Liu, C.S. Chen, The method of particular solutions for solving nonlinear Poisson problems, Computers and Mathematics with Applications, 72(2), 501-513, 2019.
- C.S. Chen, Andreas
Karageorghis, Local Kansa-RBF algorithms for elliptic boundary value problems
in annular domain, Communications in Computational Physics, 25, 41-67, 2019.
- Dan Wang, C.S. Chen, C.M. Fan, M. Li, The MAPS based on trigonometric basis functions for solving elliptic partial differential equations with variable coefficients and Cauchy-Navier equations, Mathematics and Computers in Simulation, 159, 119-135, 2019
- C.M. Fan, Y.K. Huang, C.S. Chen, S.R. Kuo, Localized method of fundamental solutions for solving two-dimensional Laplace and biharmonic equations, to appear in Engineering Analysis with Boundary Elements, 101, 188-197, 2019.
- B. Khatri Ghimire, Xinxiang Li, C.S. Chen, A.R. Lamichhane, Hybrid Chebyshev Polynomial Scheme for Solving
Elliptic Partial Differential Equations, Journal of Computational and Applied Mathematics, 364, 112324, 2020.

- D.W. Watson, A. Karageorghis, C.S. Chen, The radial basis
function-differential quadrature method for elliptic problems in annular
domains, Journal of Computational and Applied Mathematics, 363, 53-76, 2020.

- Dan
Wang, C.S. Chen, Wen Li, An efficien MAPS for solving fourth order
partial differential equations using trigonometric functions, Computers and Mathematics with Applications, 79, 934-946, 2020.

- Ji
Lin, Sergiy Reutskiy, C.S. Chen, Jun Lu, A novel method for solving
time-dependent 2D advection-diffusion-reaction equations to model
transfer in nnlinear anisotropic media, Communications in
Computational Physics, 173, 105-114, 2020.

- Wanru Chang, C.S. Chen, Xio-Yan Liu, Ming Li, Localized meshless method based on polynomial basis functions for solving axisymmetric equations, Mathematics and Computers in Simulation, 177, 487-499, 2020
- Cheng Deng, Hui Zheng, Mingfu Fu, Jingang Xiong, C.S. Chen, An efficient method of approximate particular solutions using polynomial basis functions, Engineering Analysis with Boundary Elements, 111, 1-8, 2020.
- Cheng Deng, Yan Shi, Hui Zheng, C.S. Chen, Solving fourth-order PDEs using the LMAPS, Advances in Applied Mathematics and Mechanics, 12, 920-939, 2020.
- C.S. Chen, Andreas Karageorghis, Hui Zheng, Radial basis function collocation methods for fourth order boundary value problems, Communication in Computational Physics, 27, 1530-1549, 2020.
- Xiao-yan Liu, Hui Wang, C.S. Chen, Qing Wang, Ming Li, Yong Wang, Implicit surface reconstruction with radial basis functions via PDEs, Engineering Analysis with Boundary Elements, 110, 95-103, 2020.
- C.S. Chen, Shu-Hui Shen, Fangfang Dou, LMAPS for solving four-order PDEs with polynomial basis functions, Mathematics and Computers in Simulation, 177, 500-515, 2020.
- Q. Xi, C.S. Chen, Zhou-Jia Fu, Eva Comino, The MAPS
with polynomial basis functions for solving axisymmetric time-fractional
equations, Computers and Mathematics with Applications, 88, 78-90, 2021.

- Hui Zheng, C.S. Chen, M. Lei, Yang Wang, Improved 3D surface reconstruction based on the method of fundamental solutions, Numer. Math. Theor. Meth. Appl., 13, 973-985, 2020
- C.S.
Chen, Andreas Karageorghis, Hui Zheng, Improved RBF collocation methods for
fourth order boundary value problems, Communication in Computational Physics,
27, 1530-1549, 2020.
- Yanhua Cao, C.S. Chen, Hui Zheng, Space-time polynomial particular solution method for solving time-dependent problems, Numerical Heat Transfer (Part B), 77, 181-194, 2020.
- C.S.
Chen, Andreas Karageorghis, Fangfang Dou, A novel RBF collocation
method using fictitious centers, Applied Mathematics Letters, 101,
106069, 2020.

- Xiaomin Zhu, Fangfang Dou, Andreas Karageorghis, C.S. Chen, A fictitious points one-step MPS-MFS technique, Applied Mathematics and Computation, 382, 2020, 125332.
- Andreas
Karageorghis Demetriana Tappoura, C.S. Chen, Kansa RBF method with auxiliary
boundary cetres for fourth order BVPs, Mathematics and Computers in Simulation,
181, 581-597, 2020.

- Fangfang Dou, Li-Ping Zhang, Zi-Cai Li, C. S. Chen, Source Nodes on Elliptic Pseudo-boundaries in Method of Fundamental Solutions for Laplace's Equation; Selection of Pseudo-boundaries, Journal of Computational and Applied Mathematics, 377, 112861, 2020.
- Ji
Lin, Yuxiang Zhao, Daniel Watson, C.S. Chen, The radial basis function
differential quadrature method with ghost points, Mathematics and Computers in
Simulation, 173, 105-114, 2020.
- Z.Y. Ma, X.X. Li, C.S. Chen, Ghost point method using RBFs and polynomial basis functions, Applied Mathematics Letters, 111, 106618, 2021.
- Zhuo-Chao Tang, C.S. Chen, Zhou-Jia Fu, A localized MAPS using polynomial basis functions for the fourth order concave-shape plate bending equations, Archive of Applied Mechanics, 90(10), 2241-2253, 2021.
- C.S. Chen, Malgorzata A. Jankowska, Andreas Karageorghis, RBF-DQ algorithms for
elliptic problems in axisymmetric domains, Numerical Algorithms, 2021. online https://doi.org/10.1007/s11075-021-01105-w

- D.L. Young, Shin-Ruei Lin, Chuin-Shan Chen, C.S. Chen, Two--step MPS--MFS
ghost point method
for solving partial differential equations, Computers and Mathematics with Applications, 94, 38-46, 2021.

- C.S.
Chen, Lionel Amuzu, Kwesi Acheampong, Huiqing Zhu, Improved geometric modeling
using the method of fundamental solutions, Engineering Analysis with Boundary Elements, 130, 49-57, 2021.

- C.S.
Chen, A. Karageorghis, Lionel
Amuzu, Kansa RBF method with auxiliary boundary
centres for high order BVP, to appear in Journal of Computational and
Applied Mathematics, 398, 113680, 2021. https://doi.org/10.1016/j.cam.2021.113680.

- Hui
Zheng, Zhuowan Fan, Jichun Li, C.S. Chen, A meshfree RBR
collocation method for negative reflections of electromagetic wave
propagation in metamaterials, submitted.

__Refereed
Conference Proceeding__

1.
C.Y.
Chan and C. S. Chen, A nonlinear singular parabolic initial boundary
value
problem, ed. V. Lakshmikantham,
*Nonlinear Analysis and Applications***,** Marcel Dekker, New York, 1987, pp
115-119.

*2.
*A. Muleshkov
and C.S. Chen, A note on the critical length for mixed boundary value
problems,
*Proceedings** of the
First International Conference on Dynamic System and Applications*,
1,
271-276, 1994*.*

*3.
*C.S. Chen
and M. Golberg,
A domain embedding method and the quasi-monte
carlo
method for Poisson's Equation,
*Boundary Elements XVII***,**
Computational Mechanics Publications,
Boston, Southampton, 1995, 115-122.* *

4.
C.Y.
Chan and C.S. Chen, Method of fundamental solutions for
multi-dimensional
quenching problems, *Proceeding of Dynamic
Systems and Applications*, 2, ed. G.S. Ladde
and
M. Sambandham, 1996,
115-121.

5.
C.S.
Chen and M.A. Golberg,
Las Vegas method for diffusion
equations, *Boundary Element Technology
XII*, eds. J.I. Frankel, C.A. Brebbia
& M.A.H.
Aliabadi, Computational
Mechanics Publications, 1997,
299-308.

6.
C.S. Chen
and C.A. Brebbia,
The dual reciprocity method for Helmholtz-type operators, *Boundary Element Method XX ,*
eds. A.
Kassab, C.A. Brebbia, M. Chopra, Computationa
Mechanics Publications, 1998, 495-504.

7.
M. Marcozzi, S. Choi and C.S. Chen,
RBF and optimal stopping
problems; an application to the pricing of Vanilla options on one risky
asset, *Boundary Element Technology XIII*,
eds.
C.S. Chen, C.A. Brebbia,
D.W. Pepper, WIT Press,
Boston, Southampton, pp. 345-354, 1999.

8.
C.S.
Chen, M. Marcozzi and
S. Choi, The method of
fundamental solutions and compactly supported radial basis functions -
a meshless approach to
3D problems, *Boundary Element Methods XXI*,
eds. C.A. Brebbia,
H. Power, WIT Press, Boston, Southampton, pp. 561-570, 1999.

9.
C.S.
Chen, A.S. Muleshkov
and M.A. Golberg,
The numerical evaluation of particular solutions for Poisson's equation
- a
revisit, *Boundary Element Methods XXI*,
eds. C.A. Brebbia, H.
Power, WIT Press, Boston,
Southampton, pp. 313-322, 1999.

10.
M.A. Golberg, C.S. Chen &
A.S. Muleshkov,
The method of fundamental solutions for diffusion equations, *Boundary Element Technology XIII*, eds.
C.S. Chen, C.A. Brebbia,
D.W. Pepper, WIT Press,
Boston, Southampton, pp. 377-386, 1999.

11.
Y.F. Rashed, C.S. Chen and M.A. Golberg,
Equivalent boundary integrals for Boussinesq
- Cerruti half
interaction with thin plates, *Boundary
Element Methods XXI*, eds. C.A. Brebbia,
H. Power, WIT Press, Boston, Southampton, pp.
615-625, 1999.

12.
A.H.-D.
Cheng, C.S. Chen, M.A. Golberg
and D.-L. Young,
Radial basis functions, polynomial basis functions, particular
solutions and
DRBEM, 14th Engineering Mechanics Conference, Austin, Texas, May 21-24,
2000
(in CD ROM).

13.
C.S.
Chen, M.A. Golberg, M. Ganesh, A. H-D. Cheng,
The dual reciprocity method using multilevel method compactly supported
radial
basis functions, *Boundary Element Methods
XXII*, eds. C.A. Brebbia,
H. Power, WIT Press,
Boston, Southampton, pp. 555-564, 2000

14.
A.S. Muleshkov, C.S. Chen, M.A. Golberg
and A.H-D. Cheng, Analytic particular solutions for inhomogeneous
Helmholtz-type equations, *Advances in
Computational Engineering & Sciences*, eds. S.N. Atluri,
F.W. Brust, Tech
Science Press, Vol. 1, pp. 27-32,
2000.

15.
M.A. Golberg, C.S. Chen and V. Popov,
A mesh free method for
nonlinear reaction-diffusion equation, *Advances
in Computational Engineering & Sciences*, eds. S.N. Atluri,
F.W. Brust, Tech
Science Press, Vol. 1, pp. 2-7, 2000

16.
J. Jerko, C.S. Chen, B. Sarler, A polygone-free to steady natural
convection in solid-liquid
systems, *Moving Boundaries VI*, ed.
B.
Sarler and C.A. Brebbia,
WIT Press, Southampton, pp. 112-122, 2001

17.
Xin Li,
C.H. Ho and C.S. Chen, Computational test of approximation of functions
and
their derivatives by radial basis functions,*
Advances in Computational Engineering & Sciences*,
eds. S.N. Atluri, T. Nishioka, M. Kikuchi,
Tech Science Press, Los Angels,
CD-ROM, # 76,
2001.

18.
M. Ludian, Jichun
Li and C.S. Chen,
The DRM using Helmholtz-type operators, *Advances
in Computational Engineering & Sciences*, eds. S.N. Atluri,
T. Nishioka, M.
Kikuchi, Tech Science Press, Los Angels,
CD-ROM, # 77, 2001.

19.
C.J.S. Alves, C.S. Chen, The MFS method
adapted for a non homogeneous
equation,* Advances in Computational
Engineering & Sciences*, eds. S.N. Atluri, T. Nishioka, M. Kikuchi,
Tech Science Press, Los Angels,
CD-ROM, # 135, 2001

20.
B. Sarler, J. Perko and C.S. Chen, A
meshless approach for
natural convection, *Advances in Computational
Engineering &
Sciences*, eds. S.N. Atluri,
T. Nishioka, M.
Kikuchi, Tech Science Press, Los Angels,
CD-ROM, # 150, 2001.

21.
C.J.S. Alves, C.S. Chen and B. Sarler,
The method of fundamental solutions for solving Poisson problems,
Boundary
Elements XXIV, eds. C.A. Brebbia,
A. Tadeu and V. Popov,
WIT Press, Southampton, Boston, pp.
67-76, 2002.

22.
A.S. Muleshkov, M.A. Golberg, A.H-D.
Cheng and C.S.
Chen, Polynomial
particular solutions for Poisson problems, *Boundary
Elements XXIV*, eds. C.A. Brebbia,
A. Tadeu and V. Popov,
WIT Press, Southampton, Boston, pp.
115-124, 2002.

23.
J. Li,
C.S. Chen, D. Pepper and Y. Chen, Mesh-free method for groundwater
modeling,
Boundary Elements XXIV, eds. C.A. Brebbia,
A. Tadeu and V. Popov,
WIT Press, Southampton, Boston, pp.
145-154, 2002.

24.
D.W. Pepper, C.S. Chen ,
A meshless method for
modeling heat transfer, *Advances in
Computational Engineering &
Sciences*, eds. S.N. Atluri,
D.W. Pepper, Tech
Science Press, Los Angels,
#156, 2002.

25.
B. Sarler, R. Vertnik; M. Savic, C.S. Chen, A meshless
approach for hallow-brick temperature field, *Advances
in Computational Engineering & Sciences*, eds. S.N. Atluri, D.W. Pepper, Tech
Science Press, Los Angels,
#154, 2002.

26.
B. Sarler,
J. Perko and C.S. Chen,
Natural convection in Porous Media
-radial basis function collocation method solution of the Darcy model,
to
appear in Fifth World Congress on Computational Mechanics, 2002.

27.
D.W.
Pepper, C.S. Chen and Jichun
Li, Modeling heat
transfer using adaptive finite elements, boundary elements, and meshless methods, in Advanced
Computational Methods in Heat
Transfer, eds. B. Sunden
and C.A. Brebbia,
WIT Press, Southampton, Boston, 2002.

28.
Jichun Li, A.
D.-H. Cheng and C.S. Chen, On
the efficiency and
exponential convergence of multiquadric
collocation
methods compared with finite element method, *Eng.
Anal. with Boundary
Elements*, 27, pp.
251-257, 2003.

29.
M. S. Ingber and C. S, Chen, A
parallel domain decomposition
approach for solving diffusion equations using the method of
fundamental
solutions, in Proceedings of the 6th ASME-JSME Thermal Engineering
Joint
Conference, AJTEC2003, Hawaii Island, Hawaii, Japan Society of
Mechanical
Engineers (2003).

30.
A.S. Muleshkov, M.A. Golberg, C.S.
Chen, The method of fundamental solutions for solving the axisymmetric
Poisson
equation, *Advances in Computational &
Experimental Engineering & Sciences*, eds. S.N.
Atluri, D.E. Beskos; D. Polyzos, 2003.

31.
Xin Li,
C.S. Chen, Computation of particular solutions by Hyperinterpolation
and Fast Fourier Transform, *Advances in
Computational & Experimental Engineering & Sciences*,
eds. S.N.
Atluri,, D.E. Beskos; D. Polyzos, 2003, CD-ROM.

32.
B. Sarler, I. Kovacevic,
and C.S. Chen, A mesh-free solution of temperature in direct-chill cast
slabs
and billets. V: MAMMOLI, A.A. (ed.), BREBBIA, Carlos Alberto (ed.). Moving boundaries VII
computational modeling of free
and moving boundary problems, (Computational and experimental methods,
vol.
10). Southampton, Boston: WIT Press, 2003, pp.271-280.

33.
Valjean Elander, C. S. Chen, Darrell
Pepper, The Method of
Fundamental Solutions for Axi-symmetric
Problems,
2003 ASME Summer Heat Transfer Conference Proceeding, CD ROM.

34.
A. Tadeu, L. Godinho, C. S. Chen,
Performance of the BEM, MFS, and RBF Collocation Method in a 2.5D wave
propagation analysis, Boundary Elements XXVII, eds. A.
Kassab, C.A. Brebbia, E. Divo, and D. Poljak,
p.143-153, 2005.

35.
B. Sarler, T. Tran-Cong, C.S. Chen,
Meshfree
direct and indirect local radial basis function collocation
formulations for
transport phenomena, Boundary Elements XXVII, eds. A.
Kassab, C.A. Brebbia, E. Divo, and D. Poljak,
p.417-427, 2005.

36.
J. Li,
C.S. Chen, Y.C. Hon, Radial basis meshless
methods
for unsaturated flow problems, Boundary Elements XXVII, eds. A.
Kassab, C.A. Brebbia, E. Divo, and D. Poljak, p.25-35,
2005.

37.
B. Sarler, Janez
Perko,
C.S. Chen, Numerical
Diffusion of Meshless
Diffuse Approximate Method, International Conference on Computational
&
Experimental Engineering, CD-ROM, 2006.

38.
H.Y. Tian, S. Reutskiy,
and C.S. Chen, New basis functions and their
applications to PDEs, Proceedings of International Conference on
Computational
& Experimental Engineering and Sciences, 851-857, 2007.

39.
R. Gospavic, N. Haque, V. Popov,
C.S. Chen, Comparison of two solvers for the extended method of
fundamental
solutions, Boundary
Elements and Other Meshless
Reduction Method XXX, eds. P. Skerget
and C.A. Brebbia, p.
191-199, 2008.

40.
Guangming Yao,
C.S. Chen, Marina Jelen,
Bozidar Sarler, Meshless solutions
of temperature fields for use in dendritic growth simulations, Proceedings
of the International Conference on Optimization using Exergy-Based
Methods and Computational Fluid Dynamics, Berlin, Germany, October
20-23, 2009.

41.
Wataru
Fujisaki, C.S. Chen, Suitable allocation of collocation/sources for
notched
plate problems by the MFS, Proceeding of Computational Engineering
Conference,
Vol. 19, 2014.

42.
A. Karageorghis, C.S. Chen, A
Kansa-RBF method for Poisson
problems in annular domain, Proceeding of BEM/MRM 37, 2014.

43.
Ji Lin,
Wen Chen, C.S. Chen, Fast evaluation of the method of fundamental
solutions for
solving reaction diffusion problems, Conference Proceeding of Third International
Conference on
Computational Methods for Thermal Problems, THERMACOMP2014,
editors: B. Sarler, N. Massarotti,
P. Nithiarasu, p.
263-266, 2014.

44.
Xiao-Yan
Liu, Wen Li and C.S. Chen, Fast matrix decomposition method for solving
Poisson
problems, Conference Proceeding of International Conference on
Computational Methods for
Thermal Problems, THERMACOMP2014, editors:
B. Sarler,
N. Massarotti, P. Nithiarasu,
p. 275-278, 2014.

45.
P.H.
Wen, C.S. Chen, Y.C. Hon, M. Li, Finite integration method for solving
multi-dimensional partial differential equations, ICCM 2014.