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Efficient iterative method for solving optimal control problem governed by diffusion equation with time fractional derivative. (English) Zbl 1416.65272

Summary: We solve finite-difference approximations of a linear-quadratic optimal control problem governed by Dirichlet boundary value problem with fractional time derivative. The state equation of the problem is approximated using locally one-dimensional difference schemes. The stability estimates of discrete state equations necessary for studying the convergence of iterative solution methods for the constructed discrete optimal control problems are proved. The rate of convergence of the proposed iterative method is obtained and the optimal iterative parameter is found. The results of numerical tests for a model problem are presented.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
49M25 Discrete approximations in optimal control
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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