Iterative dynamic programming for solving linear and nonlinear differential equations

Abstract

In this paper we solve a wide range of nth order ordinary nonlinear differential equations<br><br>with initial conditions by using iterative dynamic programming. First we transform<br><br>the problem to a first order system of ordinary nonlinear differential equations,<br><br>and then transform it to an optimal control problem. By the optimal solution of the<br><br>problem we obtain a piecewise-constant optimal control function and then by using<br><br>the approximate control signals, we obtain the approximate optimal trajectory. Finally,<br><br>we calculate the error functional E.