A Comparative Study of Particle Swarm Optimization and Artificial Bee Colony Algorithm for Numerical Analysis of Fisher’s Equation

Abstract

The aim of this research work is to obtain the numerical solution of Fisher’s equation using the radial basis function (RBF) with pseudospectral method (RBF-PS). The two optimization techniques, namely, particle swarm optimization (PSO) and artificial bee colony (ABC), have been compared for the numerical results in terms of errors, which are employed to find the shape parameter of the RBF. Two problems of Fisher’s equation are presented to test the accuracy of the method, and the obtained numerical results are compared to verify the effectiveness of this novel approach. The calculation of the error norms leads to the conclusion that the performance of PSO is better than the ABC algorithm to minimize the error for the shape parameter in a given range.