SPACE-TIME SPECTRAL METHOD FOR AN OPTIMAL CONTROL PROBLEM GOVERNED BY A TWO-DIMENSIONAL PDE CONSTRAINT

被引：0

作者：

Rezazadeh, Arezou ^{[1
]}

Darehmiraki, Majid ^{[2
]}

机构：

[1] Univ Qom, Dept Math, Qom 37161466711, Iran

[2] Behbahan Khatam Alanbia Univ Technol, Dept Math, Behbahan, Khouzestan, Iran

来源：

TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE | 2024年 / 178卷 / 01期

关键词：

Optimal control problem; Partial differential equations; Parabolic equations; Space-time spectral method; Legendre-Galerkin method; 2ND-ORDER;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we solve a two-dimensional optimal control problem with a parabolic partial differential equation (PDE) constraint. First, the space-time spectral method is used to discretize time derivative and space derivative. Then the aforementioned problem is transformed into a solvable algebraic system. Since the spectral methods converge spectrally in both space and time, they have gained a significant attention in the last few decades. We prove that our method has exponential rates of convergence in both space and time.

引用

页码：115 / 127

页数：13

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