Year: 2019
Author: Alexander Lapin, Shuhua Zhang, Sergey Lapin, Na Yan
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 6 : pp. 1358–1375
Abstract
We consider an optimal control problem which serves as a mathematical model for several problems in economics and management. The problem is the minimization of a continuous constrained functional governed by a linear parabolic diffusion-advection equation controlled in a coefficient in advection part. The additional constraint is non-negativity of a solution of state equation. We construct and analyze several mesh schemes approximating the formulated problem using finite difference methods in space and in time. All these approximations keep the positivity of the solutions to mesh state problem, either unconditionally or under some additional constraints to mesh steps. This allows us to remove corresponding constraint from the formulation of the discrete problem to simplify its implementation. Based on theoretical estimates and numerical results, we draw conclusions about the quality of the proposed mesh schemes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0186
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 6 : pp. 1358–1375
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Mean field game optimal control problem parabolic diffusion-advection equation finite difference methods.
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