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

TL;DR

This paper introduces a numerical method combining trigonometric cubic B-spline collocation and Crank-Nicolson schemes to efficiently approximate solutions of Fisher's equation, a key model in population biology.

Contribution

The study develops a novel numerical approach that enhances accuracy and efficiency in solving Fisher's equation compared to existing methods.

Findings

High accuracy of the proposed method demonstrated through numerical results

The technique is a viable alternative to traditional methods for Fisher's equation

Efficient handling of spatial and temporal discretization in population models

Abstract

In this study, we set up a numerical technique to get approximate solutions of Fisher's equation which is one of the most important model equation in population biology. We integrate the equation fully by using combination of the trigonometric cubic B-spline functions for space variable and Crank-Nicolson for the time integration. Numerical results have been presented to show the accuracy of the current algorithm. We have seen that the proposed technique is a good alternative to some existing techniques for getting solutions of the Fisher's equation.