On the Convergence of the MFS-MPS Scheme for 1D Poisson's Equation
The method of fundamental solutions (MFS) has been an effective meshless method for solving homogeneous partial differential equations. Coupled with radial basis functions (RBFs), the MFS has been extended to solve the inhomogeneous problems through the evaluation of the approximate particular solution and homogeneous solution. In this paper, we prove the the approximate solution of the above numerical process for solving 1D Poisson's equation converges in the sense of Lagrange interpolating polynomial using the result of Driscoll and Fornberg .
International Journal of Computational Methods
(2013). On the Convergence of the MFS-MPS Scheme for 1D Poisson's Equation. International Journal of Computational Methods, 10(2).
Available at: http://aquila.usm.edu/fac_pubs/7727