A Nonlinear Partial Integro-differential Equation Arising in Population Dynamic Via Radial Basis Functions and Theta-method

Volume 13, Issue 1, pp 14-25 http://dx.doi.org/10.22436/jmcs.013.01.02

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Authors

M. Aslefallah - Department of Mathematics, Imam Khomeini International University, Qazvin, Iran. E. Shivanian - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

Abstract

This paper proposes a numerical method to deal with the integro-differential reaction-diffusion equation. In the proposed method, the time variable is eliminated by using finite difference \(\theta\)−method to enjoy the stability condition. The method benefits from collocation radial basis function method, the generallized thin plate splines (GTPS) radial basis functions are used. Therefore, it does not require any struggle to determine shape parameter. The obtained results for some numerical examples reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems.

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Keywords

• Integro-differential equation
• Radial basis functions
• Kansa method
• Finite differences \(\theta\)-method.

MSC

•  92D25
•  45K05
•  35R11

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