An orthogonal symbiotic organisms search algorithm to determine approximate solution of systems ofordinary differential equations

Abstract

Determining exact solution of systems of ordinary differential equations (ODEs) is a challenging task in many real-life problems of science and engineering. In this paper, an attempt is made to determine approximate solutions for such complicated ODEs. The Fourier series expansion is used as an approximator. The coefficients of Fourier series expansion are determined by nature-inspired algorithms. The Symbiotic Organism Search (SOS) is an evolutionary algorithm proposed by Cheng and Prayogo in 2014. It is inspired by natural phenomenon of organisms interaction in an ecosystem for their survival. Recently, Panda and Pani in 2017 reported an Orthogonal SOS (OSOS) algorithm by incorporating orthogonal array strategies in SOS, which enhances the exploration capability of original algorithm. Here, the OSOS algorithm is used to compute the coefficients of Fourier series. Simulation studies on two real-life examples using systems of ODEs reported superior performance of the proposed OSOS learning over the same model trained by three recently reported nature-inspired algorithms OCBO, OPSO, and WCA in terms of close response matching and minimal generalized distance achieved. � Springer Nature Singapore Pte Ltd. 2019.