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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

    M. Khaksarfard & Y. Ordokhani

  2. Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran

    E. Babolian

Authors
  1. M. Khaksarfard
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  2. Y. Ordokhani
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  3. E. Babolian
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Correspondence to Y. Ordokhani.

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Khaksarfard, M., Ordokhani, Y. & Babolian, E. An approximate method for solution of nonlocal boundary value problems via Gaussian radial basis functions. SeMA 76, 123–142 (2019). https://doi.org/10.1007/s40324-018-0165-1

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  • DOI: https://doi.org/10.1007/s40324-018-0165-1

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