A numerical approach for solving optimal control problem of fractional order vibration equation of large membranes

چکیده مقاله

The purpose of this study is to introduce a computational method for solving the two-dimensional optimal control problem of the large membrane vibration equation of fractional order. Our proposed approach utilizes Chebyshev cardinal functions in two dimensions to obtain a finite dimensional optimal control problem. This problem is then solved using the Lagrange multipliers method by substituting the expansions of the state and control variables in terms of two-dimensional Chebyshev cardinal functions into the objective function, dynamical system, and initial conditions. The utilization of Chebyshev nodes offers a distinct advantage by effectively mitigating the Runge phenomenon, characterized by the undesirable oscillation and divergence of high-degree polynomial interpolants in close proximity to the interval's endpoints. We extensively discuss the convergence of our method and evaluate its accuracy using three test problems. Our results demonstrate that this technique provides highly accurate numerical solutions for these types of problems.