An accurate and straightforward method for solving optimal control problems using the second-order finite difference formula

In this paper, a simple and highly accurate approximate method for solving optimal control problems (OCPs) is presented. In this method, initially, by using the necessary optimality conditions based on the Pontryagin's maximum principle, the given OCP is transformed into a two-point boundary value problem (BVP). Then, by applying a second order finite difference formula, the resulting BVP is discretized, and a system of algebraic equations is formulated. Convergence analysis of the proposed method is also discussed, and matrix formulations are provided for ease of implementation. The numerical results obtained in this study are compared with some other methods, demonstrating the high accuracy, speed, and efficiency of the proposed method for solving both linear and nonlinear OCPs.