Optimal control problem of reaction-diffusion economic system

A computationally efficient methodology is proposed to solve infinite horizon intertemporal optimization problem which appears in the areas of management and economics. Such a problem involves local instability emerging from the interaction of the discount rate in future. An algorithm based on modal space reduction and state parameterization is designed which approximates the performance functional of the problem. A numerical example is provided to demonstrate the applicability and efficiency of the proposed approach. Here, we identify values of some parameters for which our computational procedure is stable. The identified values conform to the analytic theory of the problem.