Operational Spline Scaling Functions Method for Solving Optimal Control Problems

Abstract

In this paper, a general expression formula for Spline Scaling Functions (SSFs) operational matrix of derivative is constructed. Then it is used to study a new iterative parameterization direct technique for treating optimal control problems approximately. Optimal control problems describe several important phenomena in mathematical science. In the present technique, an operational matrix of derivatives for such functions is constructed for resolving the optimal control problem. Since the obtained operational matrix of derivative comprises, many zeros elements, it can bring about a numerical accurate result with high reliability of achieving the desired results. An attractive product operation matrix of SSFs with other properties is also included in this work. With solving some examples, the comparison with the actual solutions shows that our algorithm is acceptable.