Solving systems of ordinary differential equations using differential evolution algorithm with the best base vector of mutation scheme

Abstract

A general algorithm is presented to approximately solve a great variety of systems of ordinary differential equations (ODEs) independent of their form, order, and given conditions. The systems of ODEs are formulated as optimization problem because it isn't an easy way to get the exact solution for systems of ODEs. Therefore, approximate solution is needed for solving systems of ODEs. One of the approaches used in this paper is using Fourier series expansion to approximate solutions of system of ODEs. The Differential Evolution (DE) algorithm, classified as a metaheuristic algorithm, is used as an optimization method to estimate the most accurate coefficients of Fourier series expansion. In this case, DE will be used to minimize the residual functions of the system of ODEs with Fourier series approximations. The original DE is made by putting the best base vector into the mutation part of the DE algorithm. The results show good performance of DE in solving system of ODEs.