Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 19 (2024), 143 -- 161

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This work is licensed under a Creative Commons Attribution 4.0 International License.

AN EFFICIENT AND ACCURATE MODIFIED ADOMIAN DECOMPOSITION METHOD FOR SOLVING THE HELMHOLTZ EQUATION WITH HIGH-WAVENUMBER

Saleem Nasser Alomari and Yahya Qaid Hasan

Abstract. This paper presents a modified Adomian decomposition method (MADM) for solving the one and two-dimensional Helmholtz equation with large wavenumbers. The standard Adomian decomposition method (ADM) suffers from severe divergence issues as the wavenumber increases, which limits its applicability for high-frequency problems. MADM overcomes this drawback by introducing a novel modification technique that enhances the convergence and accuracy of the solution. Several numerical examples are provided to demonstrate the effectiveness and superiority of MADM over ADM for solving the Helmholtz equation with various boundary conditions and wavenumbers.

2020 Mathematics Subject Classification: 35J05.
Keywords: Helmholtz equation; modified Adomian decomposition method; large wavenumbers.

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Saleem Nasser Alomari (corresponding author)
Department of Mathematics, Faculty of Education and Sciences,
Albaydha University, Albaydha, Yemen.
E-mail: saleemnasser86@gmail.com

Yahya Qaid Hasan
Department of Mathematics, Faculty of Applied Sciences,
Thamar University, Thamar, Yemen.
E-mail: yahya217@yahoo.com

http://www.utgjiu.ro/math/sma