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Numerical simulation of Fisher's type equation via a collocation technique based on re-defined quintic B-splines

Neeraj Dhiman (Department of Mathematics, Graphic Era Hill University, Dehradun, India)
Amit Chauhan (Department of Mathematics, Graphic Era (Deemed to be University), Dehradun, India) (Department of Mathematics, D.B.S. (P.G.) College, Dehradun, India)
Mohammad Tamsir (Department of Mathematics, Graphic Era (Deemed to be University), Dehradun, India) (Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia)
Anand Chauhan (Department of Mathematics, Graphic Era (Deemed to be University), Dehradun, India)

Multidiscipline Modeling in Materials and Structures

ISSN: 1573-6105

Article publication date: 4 April 2020

Issue publication date: 16 September 2020

145

Abstract

Purpose

A collocation technique based on re-defined quintic B-splines over Crank-Nicolson is presented to solve the Fisher's type equation. We take three cases of aforesaid equation. The stability analysis and rate of convergence are also done.

Design/methodology/approach

The quintic B-splines are re-defined which are used for space integration. Taylor series expansion is applied for linearization of the nonlinear terms. The discretization of the problem gives up linear system of equations. A Gaussian elimination method is used to solve these systems.

Findings

Three examples are taken for analysis. The analysis gives guarantee that the present method provides much better results than previously presented methods in literature. The stability analysis and rate of convergence show that the method is unconditionally stable and quadratic convergent for Fisher's type equation. Moreover, the present method is simple and easy to implement, so it may be considered as an alternative method to solve PDEs.

Originality/value

This work is the original work of authors which is neither published nor submitted anywhere else for publication.

Keywords

Acknowledgements

The authors would like to express their sincere thanks to the anonymous referees for their valuable suggestions towards improvement of manuscript.

Citation

Dhiman, N., Chauhan, A., Tamsir, M. and Chauhan, A. (2020), "Numerical simulation of Fisher's type equation via a collocation technique based on re-defined quintic B-splines", Multidiscipline Modeling in Materials and Structures, Vol. 16 No. 5, pp. 1117-1130. https://doi.org/10.1108/MMMS-09-2019-0166

Publisher

:

Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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