Comparing the effect of implicit and explicit methods on solving optimal control problem

In order to solve an optimal control problem of the form numerically, there are different explicit and implicit one-step or multi step, numerical methods such as 4th order, explicit Runge- Kutta, other explicit Runge- Kutta methods of order 2 and 3,2nd order implicit trapezoidal method and first order method. Some of there methods which are implicit are A-stable methods, whereas, explicit methods have stability regions only as an area on the left hand side of the complex plane. The aim of this paper, is to compare the effect of implicit and explicit methods on solving optimal control problems of the form (1), also the CPU time of the used method have been compared as well as optimal plots and optimal values of the problem.