Applications of particle swarm optimization for numerical simulation of Fisher’s equation using RBF

Abstract

This research article focused on optimising the parameter related to radial basis function (RBF) by solving the Fisher’s equation numerically. To obtain the numerical solutions, Particle Swarm Optimisation (PSO) algorithm is used along with radial basis functions (RBFs). PSO has been used by a number of researchers to obtain the optimised results in various scientific applications. In this work, using RBF-pseudospectral method, partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs) then are solved in MATLAB using the ODE solver. Two numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method by computingL∞, L2, and Lrms error norms with their order of convergence. Also, it can be demonstrated from the tables that the obtained results are in conformity with the results available in the literature.

Keywords

• Fisher's equation
• Particle Swarm Optimisation
• Pseudo-spectral technique
• Radial basis function