An approximate method for solution of nonlocal boundary value problems via Gaussian radial basis functions

• M. Khaksarfard ^[1] ; Y. Ordokhani ^[1] ; E. Babolian ^[2]
  1. [1] Universidad de Alzahra
  2. [2] Universidad de Kharazmi
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 76, Nº. 1, 2019, págs. 123-142
• Idioma: inglés
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• Resumen

  • In this paper, we convert the parabolic and hyperbolic partial differential equations with initial and integral boundary conditions into classical Dirichlet initial-boundary value problems. We use a new scheme to solve the nonlocal initial-boundary value problems using collocation points and approximating the solution using radial basis functions (RBFs). We introduce radial basis functions and a new operational matrix of derivative for Gaussian (GA) radial basis functions is employed to reduce the problem to a set of algebraic equations. The results of numerical experiments are presented and compared with the results of other methods to confirm the validity of this method.