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RBF-FD Method for Some Dispersive Wave Equations and Their Eventual Periodicity

Marjan Uddin1,*, Hameed Ullah Jan1,*, Muhammad Usman2
1 Department of Basics Sciences, UET, Peshawar, Pakistan.
2 Department of Mathematics, University of Dayton, Dayton, USA.
* Corresponding Authors: Marjan Uddin. Email: ;
  Hameed Ullah Jan. Email: .
(This article belongs to this Special Issue: Numerical Methods for Differential and Integral Equations)

Computer Modeling in Engineering & Sciences 2020, 123(2), 797-819. https://doi.org/10.32604/cmes.2020.08717

Received 30 September 2019; Accepted 19 December 2019; Issue published 01 May 2020

Abstract

In this paper, we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of (IBVPs) for some dispersive wave equations on a bounded domain corresponding to periodic forcing. The constructed numerical scheme is based on radial kernels and local in nature like finite difference method. The temporal variable is executed through RK4 scheme. Due to the local nature and sparse differentiation matrices our numerical scheme efficiently recovers the solution. The results achieved are validated and examined with other methods accessible in the literature.

Keywords

RBFs meshless methods,RBF-FD scheme, eventual periodicity,BBM and KdV type equations.

Cite This Article

Uddin, M., Jan, H. U., Usman, M. (2020). RBF-FD Method for Some Dispersive Wave Equations and Their Eventual Periodicity. CMES-Computer Modeling in Engineering & Sciences, 123(2), 797–819.

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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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