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Mathematical Problems in Engineering
Volume 2018, Article ID 6143934, 18 pages
https://doi.org/10.1155/2018/6143934
Research Article

Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations

1Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
2Department of Mathematics, National College of Business Administration and Economics, Lahore 54000, Pakistan

Correspondence should be addressed to Muhammad Abbas; kp.ude.sou@sabba.m

Received 17 August 2017; Revised 5 November 2017; Accepted 13 December 2017; Published 18 January 2018

Academic Editor: Chaudry M. Khalique

Copyright © 2018 Imtiaz Wasim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this study, we introduce a new numerical technique for solving nonlinear generalized Burgers-Fisher and Burgers-Huxley equations using hybrid B-spline collocation method. This technique is based on usual finite difference scheme and Crank-Nicolson method which are used to discretize the time derivative and spatial derivatives, respectively. Furthermore, hybrid B-spline function is utilized as interpolating functions in spatial dimension. The scheme is verified unconditionally stable using the Von Neumann (Fourier) method. Several test problems are considered to check the accuracy of the proposed scheme. The numerical results are in good agreement with known exact solutions and the existing schemes in literature.