This webpage contains the final report of Mr. Alexandru Cibotarica, a graduate student at University of Southern Mississippi, who completed a course entitled
"Meshless Methods for Solving Partial Differential Equations" under Professor C.S. Chen in fall semester 2010.
The contents of the course include the following topics:
- PDF file Matlab code
1. Radial basis functions for surface reconstruction
2. The method of approximate particular solutions
4. Numerical solutions for general elliptic partial differential equations.
The materials of the course are based on the manuscript
of a research monograph entitled “Scientific Computing
with Radial Basis Functions” and the
following book chapter and papers.
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, Y.C. Hon, R.S. Schaback, Radial Basis Functions with Scientific
Computation, Department of Mathematics, University of Southern Mississippi, 2010.
Wen, C.S. Chen, The
method of particular solution for solving scalar
wave equations, International Journal for Numerical Methods in Biomedical Engineering, 26, 1878-1889, 2010. (PDF file)
Chen, C.M. Fan, P.H. Wen, The Method of Particular Solutions for
Solving Certain Partial Differential Equations, to appear in Numerical
Methods for Partial Differential Equations. C.S.
Chen, C.M. Fan, P.H. Wen, The Method of Particular Solutions
Solving Elliptic Problems with Variable Coefficients, to appear in Journal of Computational Methods.
- Greg Fasshauer, Meshfree Approximation Methods with MATLAB, Interdisciplinary Mathematical Sciences - Vol. 6, World Scientific Publishers, Singapore, 2007.