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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board Member: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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Barycentric Jacobi Spectral Method for Numerical Solutions of the Generalized Burgers-Huxley Equation

Edson Pindza
  • Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, Canada; Department of Applied Mathematics, University of Western Ontario, London, ON, Canada
  • :
/ M. K. Owolabi
  • Department of Mathematical Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria
  • :
/ K.C. Patidar
  • Department of Mathematics and Applied Mathematics, University of the Western Cape, Bellville, South Africa
  • :
Published Online: 2017-01-20 | DOI: https://doi.org/10.1515/ijnsns-2016-0032


Numerical solutions of nonlinear partial differential equations, such as the generalized and extended Burgers-Huxley equations which combine effects of advection, diffusion, dispersion and nonlinear transfer are considered in this paper. Such system can be divided into linear and nonlinear parts, which allow the use of two numerical approaches. Barycentric Jacobi spectral (BJS) method is employed for the spatial discretization, the resulting nonlinear system of ordinary differential equation is advanced with a fourth-order exponential time differencing predictor corrector. Comparative numerical results for the values of options are presented. The proposed method is very elegant from the computational point of view. Numerical computations for a wide variety of problems, show that the present method offers better accuracy and efficiency in comparison with other previous methods. Moreover the method can be applied to a wide class of nonlinear partial differential equations.

Keywords: exponential time differencing; spectral methods; Burgers-Huxley equation; nonlinear PDEs; reaction-diffusion

MSC 2010: 65L05; 65M06; 65M20

Received: 2016-02-24

Accepted: 2016-10-31

Published Online: 2017-01-20

Published in Print: 2017-02-01

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation. Volume 18, Issue 1, Pages 67–81, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2016-0032, January 2017

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