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.

- Final Report
- 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. (PDF file 894K)
- C.S. Chen, Y.C. Hon, R.S. Schaback, Radial Basis Functions with Scientific Computation, Department of Mathematics, University of Southern Mississippi, 2010.
- P.H. 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)
- C.S. 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 for 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.