A collocation technique based on modified form of trigonometric cubic B-spline basis functions for Fisher’s reaction-diffusion equation

• Published in: Multidiscipline modeling in materials and structures 2018-10, Vol.14 (5), p.923-939
• Main Authors: Dhiman, Neeraj, Tamsir, Mohammad
• Format: Article
• Language: English
• Subjects: B spline functions; Basis functions; Collocation methods; Exact solutions; Genetic engineering; Mathematical analysis; Mathematical models; Numerical methods; Partial differential equations; Reaction-diffusion equations; Series expansion; Stability analysis; Taylor series; Tissue engineering
• ISSN: 1573-6105; 1573-6113
• DOI: 10.1108/MMMS-12-2017-0150

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.