Stable Gaussian radial basis function method for solving Helmholtz equations

Document Type : Research Paper


School of Mathematics, Iran University of Science and Technology, Tehran, Iran


‎Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems‎. ‎They are often referred to as a meshfree method and can be spectrally accurate‎. ‎In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion‎. ‎We develop our approach in two-dimensional spaces for solving Helmholtz equations‎. ‎In this paper, the eigenfunction expansions are rebuilt based on Chebyshev polynomials which are more suitable in numerical computations‎. ‎Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed method for solving two-dimensional Helmholtz equations‎.


Volume 7, Issue 1
January 2019
Pages 138-151
  • Receive Date: 17 September 2017
  • Revise Date: 25 February 2018
  • Accept Date: 27 October 2018
  • First Publish Date: 01 January 2019