Solving some ordinary differential equations numerically using differential evolution algorithm with a simple adaptive mutation scheme

Differential equations have been used to describe phenomena in many fields. However, not all of differential equations can be solved in analytic ways so there is some approach being made to solve them numerically. One of the approaches is using Fourier series expansion to approximate solutions of linear and nonlinear ordinary differential equations (ODEs). The coefficients of Fourier series expansion are estimated by an optimization method using Differential Evolution (DE). In this case, differential evolution will be used to minimize the residual function of the Fourier series that are implemented into the ordinary differential equations. A modification from the original DE is made by putting a simple adaptive scheme into the mutation part of the DE algorithm. The results show good performance of DE in solving various ODEs.