A Computational Approach for One and Two Dimensional Fisher’s Equation Using Quadrature Technique

Abstract

In this paper, a refined form of the differential quadrature method is proposed to compute the numerical solution of one and two-dimensional convection-diffusion Fisher’s equation. The cubic trigonometric B-spline basis functions are applied in the differential quadrature method in a modified form to obtain the weighting coefficients. The application of the method reduces nonlinear Fisher’s partial differential equation into a system of ordinary differential equations which can be solved by applying the Runge-Kutta method. Six numerical test problems of Fisher’s equation are analyzed numerically to establish the efficiency of the proposed method. The stability of the method is also discussed using the matrix method.

KEYWORDS AND PHRASES:

• Differential quadrature method
• trigonometric B-spline
• SSP-RK43
• Fisher’s equation
• nonlinear partial differential equation

Acknowledgements

The authors like to thanks the reviewers for the constructive comments that are helpful in the improvement of the manuscript.