Iterative dynamic programming for solving linear and nonlinear differential equations

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