Particle Swarm Optimization for Solving Nonlinear Fisher’s Equation

Abstract

The term "optimization" describes a way of increasing the favourable features of a function in a mathematical form while reducing the negative ones. Most of the problems encountered in the real world may be formulated as optimization problems. Particle swarm optimization is a tool which has been used extensively to handle problems across different fields. The purpose of this study is to develop a numerical method for solving nonlinear reaction-diffusion Fisher’s equations, whose numerical solutions exhibit the solitons form and have a wide range of applications. This study includes differential quadrature method using exponential basis function and particle swarm optimization. In the work so far documented in the literature, a random number was used to approximate the involved parameter in the basis functions. This value is now determined using the implemented optimization technique. The numerical solutions obtained for the equation is comparable to the data available in the literature. The research presented through figures and tables, yields favourable results.

Keywords

• b-spline
• particle swarm optimization (pso)
• fisher's reaction diffusion equation (frde)
• differential quadrature method (dqm)