Approximate solutions of general second–order initial value problems using differential evolution

Abstract

In this paper, it is assumed that the solution of the general second order initial value problem $u^{\prime \prime} = f\left(t, u, u^{\prime} \right);\quad u(t_0) = u_0,\;\;u^{\prime}(t_0) = u^{\prime}_0, \quad t \in \left[t_0,t_n\right]$ can be approximated by a polynomial \emph{u(t)}. To obtain the values of the coefficients of the terms of \emph{u(t)}, the problem is converted to an optimization problem and the simple stochastic function minimizer called differential evolution is used to obtain the optimal values of the coefficients. Numerical examples show the efficiency and accuracy of the proposed technique compared with some existing classical methods.

https://doi.org/10.28919/jmcs/3404