WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 22, 2023
Solving the Cauchy Problem Related to the Helmholtz Equation through a Genetic Algorithm
Authors: ,
Abstract: 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.