用遗传算法求解与亥姆霍兹方程有关的柯西问题

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2023-10-09 DOI:10.37394/23206.2023.22.79

Jamal Daoudi, Chakir Tajani

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引用次数: 0

摘要

与亥姆霍兹方程相关的柯西问题是一个病态逆问题，由于其不稳定性和对噪声的敏感性而具有挑战性。在本文中，我们提出了一种元启发式方法来解决这个问题，使用遗传算法结合吉洪诺夫正则化。即使在存在噪声的情况下，我们的方法也能够为柯西问题产生稳定，收敛和准确的解。在规则域和不规则域上的数值结果表明了该方法的有效性和准确性。

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Solving the Cauchy Problem Related to the Helmholtz Equation through a Genetic Algorithm

The Cauchy problem associated with the Helmholtz equation is an ill-posed inverse problem that is challenging to solve due to its instability and sensitivity to noise. In this paper, we propose a metaheuristic approach to solve this problem using Genetic Algorithms in conjunction with Tikhonov regularization. Our approach is able to produce stable, convergent, and accurate solutions for the Cauchy problem, even in the presence of noise. Numerical results on both regular and irregular domains show the effectiveness and accuracy of our approach.

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来源期刊

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.