Numerical solution of generalized Burger’s-Huxley equation using local radial basis functions

Bukhari, Mutia; Arshad, Muhammad; Batool, Safeera; Saqlain, Syed Muhammad

International Journal of Advanced and Applied Sciences

Int. j. adv. appl. sci.

EISSN: 2313-3724

Print ISSN: 2313-626X

Volume 4, Issue 5 (May 2017), Pages: 1-11

Title: Numerical solution of generalized Burger’s-Huxley equation using local radial basis functions

Author(s): Mutia Bukhari ^1,*, Muhammad Arshad ¹, Safeera Batool ², Syed Muhammad Saqlain ³

Affiliation(s):

¹Department of Mathematics, Islamia College University, Peshawar, Pakistan
²Department of Basic Sciences, University of Engineering & Technology, Taxila, Pakistan
³Department of Computer Science & Software Engineering, International Islamic University, Islamabad, Pakistan

https://doi.org/10.21833/ijaas.2017.05.001

Full Text - PDF XML

Abstract:

Partial differential equations are well known with their use in different areas of applied mathematics and engineering. Numerical solutions to these equations are widely accepted but the development of robust, simple and efficient numerical scheme for the solution of partial differential equations is a challenging research issue. In this Paper a local radial basis function based differential quadrature collocation method is presented. It finds the numerical solution of Generalized Burger’s Huxley equation and its various special cases such as Burger’s Huxley equation, Generalized Burger’s equation and Huxley equation. The proposed method is implemented through different examples using Gaussian radial basis functions (RBF) with central three point scheme and central five point scheme in the local support region. Accuracy of the method is investigated by computing L₂ and error norms and absolute errors. The results of the proposed technique in terms of error norms comparative to the existing techniques of adomian decomposition and global mesh free method are presented as well.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Burger’s-Huxley equation, Radial basis function, Differential collocation

Article History: Received 25 August 2016, Received in revised form 31 March 2017, Accepted 31 March 2017

Digital Object Identifier:

https://doi.org/10.21833/ijaas.2017.05.001

Citation:

Bukhari M, Arshad M, Batool S, and Saqlain SM (2017). Numerical solution of generalized Burger’s-Huxley equation using local radial basis functions. International Journal of Advanced and Applied Sciences, 4(5): 1-11

http://www.science-gate.com/IJAAS/V4I5/Bukhari.html

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