Computing and Simulation for Engineers

14 Numerical Solution of Fisher’s Equation by using Fourth-Order Collocation Scheme Based on Modified Cubic B-Splines

Brajesh Kumar Singh and Mukesh Gupta

Babasaheb Bhimrao Ambedkar University

DOI: 10.1201/9781003222255-14

CONTENTS

1. 14.1 Introduction
2. 14.2 Fourth-Order Spatial Approximation with Modified Cubic B-Splines
3. 14.3 Implementation of mCBCT4 on Fisher’s Equation
   1. 14.3.1 Initial Solution Vector for Systems
4. 14.4 Numerical Simulation of Fisher’s Equation Using mCBCT4
5. 14.5 Conclusions
6. Acknowledgment
7. References

14.1 Introduction

Fisher [1] in 1936 proposed a model for the propagation of a mutant gene in the form of nonlinear parabolic partial differential equation (PDE):

$\frac{\partial \varphi }{\partial \tau }=\nu \frac{{\partial }^2\varphi }{\partial x^2}+\rho \text{F}(\varphi (x,\tau )),x\in R,\tau \ge 0\mathrm{.}$(14.1)

where $x$ and $\tau$ are spatial ...