Numerical Solution of Arbitrary‐Order Ordinary Differential and Integro‐Differential Equations with Separated Boundary Conditions Using Optimal Control Technique

In this paper, a new method for solving arbitrary order ordinary differential equations and integro‐differential equations of Fredholm and Volterra kind is presented. In the proposed method, these equations with separated boundary conditions are converted to a parametric optimization problem subject to algebraic constraints. Finally, control and state variables will be approximated by a Chebychev series. In this method, a new idea has been used, which offers us the ability of applying the mentioned method for almost all kinds of ordinary differential and integro‐differential equations with different types of boundary conditions. The accuracy and efficiency of the proposed numerical technique have been illustrated by solving some test problems.