A collocation technique based on modified form of trigonometric cubic B-spline basis functions for Fisher’s reaction-diffusion equation
Multidiscipline Modeling in Materials and Structures
ISSN: 1573-6105
Article publication date: 20 September 2018
Issue publication date: 29 October 2018
Abstract
Purpose
The purpose of this paper is to present a modified form of trigonometric cubic B-spline (TCB) collocation method to solve nonlinear Fisher’s type equations. Taylor series expansion is used to linearize the nonlinear part of the problem. Five examples are taken for analysis. The obtained results are better than those obtained by some numerical methods as well as exact solutions. It is noted that the modified form of TCB collocation method is an economical and efficient technique to approximate the solution PDEs. The authors also carried out the stability analysis which proves that the method is unconditionally stable.
Design/methodology/approach
The authors present a modified form of TCB collocation method to solve nonlinear Fisher’s type equations. Taylor series expansion is used to linearize the nonlinear part of the problem. The authors also carried out the stability analysis.
Findings
The authors found that the proposed method results are better than those obtained by some numerical methods as well as exact solutions. It is noted that the modified form of TCB collocation method is an economical and efficient technique to approximate the solution PDEs.
Originality/value
The authors propose a new method, namely, modified form of TCB collocation method. In the authors’ best knowledge, aforesaid method is not proposed by any other author. The authors used this method to solve nonlinear Fisher’s type equations and obtained more accurate results than the results obtained by other methods.
Keywords
Acknowledgements
The authors are very thankful to the editor and reviewers for their valuable comments and suggestions to improve the quality of the paper.
Citation
Dhiman, N. and Tamsir, M. (2018), "A collocation technique based on modified form of trigonometric cubic B-spline basis functions for Fisher’s reaction-diffusion equation", Multidiscipline Modeling in Materials and Structures, Vol. 14 No. 5, pp. 923-939. https://doi.org/10.1108/MMMS-12-2017-0150
Publisher
:Emerald Publishing Limited
Copyright © 2018, Emerald Publishing Limited