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RBF Based Localized Method for Solving Nonlinear Partial Integro-Differential Equations

Marjan Uddin1, *, Najeeb Ullah2, Syed Inayat Ali Shah2
1 University of Engineering and Technology, Peshawar, Pakistan.
2 Islamia College University, Peshawar, Pakistan.
* Corresponding Author: Marjan Uddin. Email: .
(This article belongs to this Special Issue: Numerical Methods for Differential and Integral Equations)

Computer Modeling in Engineering & Sciences 2020, 123(3), 957-972. https://doi.org/10.32604/cmes.2020.08911

Received 23 October 2019; Accepted 17 February 2020; Issue published 28 May 2020

Abstract

In this work, a numerical scheme is constructed for solving nonlinear parabolictype partial-integro differential equations. The proposed numerical scheme is based on radial basis functions which are local in nature like finite difference numerical schemes. The radial basis functions are used to approximate the derivatives involved and the integral is approximated by equal width integration rule. The resultant differentiation matrices are sparse in nature. After spatial approximation using RBF the partial integro-differential equations reduce to the system of ODEs. Then ODEs system can be solved by various types of ODE solvers. The proposed numerical scheme is tested and compared with other methods available in literature for different test problems. The stability and convergence of the present numerical scheme are discussed.

Keywords

RBFs, integral equations, local method.

Cite This Article

Uddin, M., Ullah, N., Inayat, S. (2020). RBF Based Localized Method for Solving Nonlinear Partial Integro-Differential Equations. CMES-Computer Modeling in Engineering & Sciences, 123(3), 957–972.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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