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

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.

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