The Numerical Approach to the Fisher's Equation via Trigonometric Cubic B-spline Collocation Method

Abstract

In this study, we set up a numerical technique to get approximate solutions of Fisher's equation which is integrated fully with help of combination of the trigonometric cubic B-spline functions in space and Crank-Nicolson in time. Numerical results have been presented to show utility of the current algorithm by studying three test problems. Solutions of the fisher equation are shown to model the wave front numerically and interaction of diffusion and reaction is observed for the Fisher eqaution.

A Comparative Numerical Study of Parabolic Partial Integro-Differential Equation Arising from Convection-Diffusion

“…Recently, CBTS functions have been employed for the solution of PIDE problem [19,34]. The CTBS functions are also employed for the solution different problems which include Hunter Saxton equation [25], time fractional diffusion-wave equation [26], Fisher's reaction-diffusion equations [28], non-conservative linear transport problems [27], Nonclassical diffusion problems [35], Hyperbolic telegraph equation [36], Fisher's equations [37], and coupled Burgers' equations [38].…”

Untitled

“…One of the most interesting equation in physical phenomena is reaction-diffusion equation. Since the equationis a model equation used in biology, chemistry, metallurgy and combustion, both analytical and numerical solutions are searched to investigate new physical phenomena 25 .…”