An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm

Abstract

This paper examines the implementation of simple combination mutation of differential evolution algorithm for solving stiff ordinary differential equations. We use the weighted residual method with a series expansion to approximate the solutions of stiff ordinary differential equations. We solve the problems from an ordinary stiff differential equation for linear and nonlinear problems. Then, we also implement our method for solving stiff systems of ordinary differential equations. We find that our algorithm can approximate the exact solution of a stiff ordinary differential equation with the smallest error for each length of series that we have chosen. Thus, this approximation method, by using the optimization method of simple combination differential evolution, can be a good tool for solving stiff ordinary differential equations.

Keywords

• Stiff ordinary differential equation
• Fourier series
• Weighted residual method
• Simple combination mutation of differential evolution