具有分数阶拉普拉斯算子和状态约束的分数阶最优控制问题的一种有效而精确的数值方法

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Numerical Methods for Partial Differential Equations Pub Date : 2023-06-26 DOI:10.1002/num.23056

Jiaqi Zhang, Y. Yang

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引用次数: 0

摘要

本文基于Caffarelli-Silvestre展开，研究了一类积分形式的分数阶拉普拉斯状态约束最优控制问题的数值逼近。得到了扩展最优控制问题的一阶最优性条件。提出了一种基于加权拉盖尔多项式的扩展问题的富谱伽辽金离散格式。证明了富谱离散格式的先验误差估计。数值实验验证了该方法的有效性，并验证了理论结果。

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An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint

In this paper, we investigate the numerical approximation of an optimal control problem with fractional Laplacian and state constraint in integral form based on the Caffarelli–Silvestre expansion. The first order optimality conditions of the extended optimal control problem is obtained. An enriched spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is proposed. A priori error estimate for the enriched spectral discrete scheme is proved. Numerical experiments demonstrate the effectiveness of our method and validate the theoretical results.

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来源期刊

Numerical Methods for Partial Differential Equations 数学-应用数学

CiteScore

7.20

自引率

2.60%

发文量

审稿时长

9 months

期刊介绍： An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.