Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method

The Quasi-Reversibility Regularization Method (Q-RRM) provides stable approximate solution of the Cauchy problem of the Helmholtz equation in the Hilbert space by providing either additional information in the Laplace-type operator in the Helmholtz equation or the imposed Cauchy boundary conditions...

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Main Authors: Benedict Barnes, Isaac Addai, Francis Ohene Boateng, Ishmael Takyi
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2022/5336305
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author Benedict Barnes
Isaac Addai
Francis Ohene Boateng
Ishmael Takyi
author_facet Benedict Barnes
Isaac Addai
Francis Ohene Boateng
Ishmael Takyi
author_sort Benedict Barnes
collection DOAJ
description The Quasi-Reversibility Regularization Method (Q-RRM) provides stable approximate solution of the Cauchy problem of the Helmholtz equation in the Hilbert space by providing either additional information in the Laplace-type operator in the Helmholtz equation or the imposed Cauchy boundary conditions on the Helmholtz equation. To help bridge this gap in the literature, a Modified Quasi-reversibility Regularization Method (MQ-RRM) is introduced to provide additional information in both the Laplace-type operator occurring in the Helmholtz equation and the imposed Cauchy boundary conditions on the Helmholtz equation, resulting in a strong stable solution and faster convergence of the solution of the Helmholtz equation than the regularized solutions provided by Q-RRM and its variants methods.
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publishDate 2022-01-01
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series Journal of Mathematics
spelling doaj-art-9f3cd8477c074f6889d6533a6c3c6a132025-08-20T02:18:33ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5336305Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization MethodBenedict Barnes0Isaac Addai1Francis Ohene Boateng2Ishmael Takyi3Mathematics DepartmentMathematics DepartmentDepartment of Mathematics EducationMathematics DepartmentThe Quasi-Reversibility Regularization Method (Q-RRM) provides stable approximate solution of the Cauchy problem of the Helmholtz equation in the Hilbert space by providing either additional information in the Laplace-type operator in the Helmholtz equation or the imposed Cauchy boundary conditions on the Helmholtz equation. To help bridge this gap in the literature, a Modified Quasi-reversibility Regularization Method (MQ-RRM) is introduced to provide additional information in both the Laplace-type operator occurring in the Helmholtz equation and the imposed Cauchy boundary conditions on the Helmholtz equation, resulting in a strong stable solution and faster convergence of the solution of the Helmholtz equation than the regularized solutions provided by Q-RRM and its variants methods.http://dx.doi.org/10.1155/2022/5336305
spellingShingle Benedict Barnes
Isaac Addai
Francis Ohene Boateng
Ishmael Takyi
Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method
Journal of Mathematics
title Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method
title_full Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method
title_fullStr Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method
title_full_unstemmed Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method
title_short Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method
title_sort solving the helmholtz equation together with the cauchy boundary conditions by a modified quasi reversibility regularization method
url http://dx.doi.org/10.1155/2022/5336305
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AT francisoheneboateng solvingthehelmholtzequationtogetherwiththecauchyboundaryconditionsbyamodifiedquasireversibilityregularizationmethod
AT ishmaeltakyi solvingthehelmholtzequationtogetherwiththecauchyboundaryconditionsbyamodifiedquasireversibilityregularizationmethod