Mehdi Delkhosh

Kourosh Parand, Sobhan Latifi, Mehdi Delkhosh et al.

In this paper, a nonlinear 2D Optimal Control Problem (2DOCP) is considered. The quadratic performance index of a nonlinear cost function is endowed with the state and control functions. In this problem, the dynamic constraint of the system is given by a classical diffusion equation. This article is concerned with a generalization of Lagrangian functions. Besides, a Generalized Lagrangian Jacobi-Gauss-Radau (GLJGR)-collocation method is introduced and applied to solve the aforementioned 2DOCP. Based on initial and boundary conditions, the time and space variables t and x are considered Jacobi-Gauss-Radau points clustered on first or end of interval respectively. Then, to solve the 2DOCP, Lagrange Multipliers are used and the optimal control problem is reduced to a parameter optimization problem. Numerical results demonstrate its accuracy, efficiency, and versatility of the presented method.

Kourosh Parand, Amin Ghaderi, Mehdi Delkhosh et al.

The purpose of this research is to propose a new approach named the shifted Bessel Tau (SBT) method for solving higher-order ordinary differential equations (ODE). The operational matrices of derivative, integral and product of shifted Bessel polynomials on the interval [a, b] are calculated. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ODE to the solution of a system of algebraic equations with unknown Bessel coefficients. The comparisons between the results of the present work and other the numerical method are shown that the present work is computationally simple and highly accurate.