NUMERICAL SOLUTION OF ARBITRARY-ORDER ORDINARY DIFFERENTIAL AND INTEGRO-DIFFERENTIAL EQUATIONS VIA OPTIMAL CONTROL TECHNIQUES

In this paper a new method for solving arbitrary order ordinary differential equations and integro-differential equations of Fredholm and Volterra types is presented. In the proposed method, mentioned equations with separated boundary conditions will be converted to an optimal control problem. After approximating control and state variables by chebychev polynomials, the numerical solution will be achieved by minimizing the obtained parametric optimization problem with the algebric constraints. Numerical results are very promising