This study develops the Runge -Kutta Like Method (RKLM), which uses Pontryagin's principle to solve optimal control problems numerically using forward-backward sweep methods. It is based on the Patade and Bhalekar methodology. The RKLM's stability properties and its convergence are examined. The Forward -backward sweep algorithm and the RKLM algorithm are implemented using MATLAB code. Physical optimum control problems are solved with the RKLM. The first problem's conclusion demonstrates that, when investment declines, the capital first grow to boost production before it depreciates. The outcome of the second problem demonstrates that a larger weight parameter causes the harvesting rate to reach zero more quickly and the total fish mass to reach its maximum level more quickly. The findings obtained demonstrate the effectiveness of using RKLM in conjunction with forward-backward sweep methods to solve optimal control problems.