Efficient numerical solution of Fisher's equation by using B-spline method

Abstract

This paper seeks to develop an efficient B-spline scheme for solving Fisher's equation, which is a nonlinear reaction–diffusion equation describing the relation between the diffusion and nonlinear multiplication of a species. To find the solution, domain is partitioned into a uniform mesh and then cubic B-spline function is applied to Fisher's equation. The method yields stable and accurate solutions. The results obtained are acceptable and in good agreement with some earlier studies. An important advantage is that the method is capable of greatly reducing the size of computational work.

Keywords:

• cubic B-spline
• Fisher's equation
• local and nonlocal boundary conditions
• tridiagonal system
• Thomas algorithm

2000 AMS Subject Classifications:

• 65M06
• 35K57

Acknowledgements

The author Ms. Geeta Arora thankfully acknowledges the financial assistance provided by MHRD grant given by IIT Roorkee, India.