Barnes, Benedict and Boateng, F and Amponsah, S and Osei-Frimpong, E (2017) On the Notes of Quasi-Boundary Value Method for Solving both Cauchy-Dirichlet Problem of the Helmholtz Equation. British Journal of Mathematics & Computer Science, 22 (2). pp. 1-10. ISSN 22310851
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Abstract
The Cauchy-Dirichlet problem of the Helmholtz equation yields unstable solution, which when solved with the Quasi-Boundary Value Method (Q-BVM) for a regularization parameter α = 0. At this point of regularization parameter, the solution of the Helmholtz equation with both Cauchy and Dirichlet boundary conditions is unstable when solved with the Q-BVM. Thus, the quasi-boundary value method is insufficient and inefficient for regularizing ill-posed Helmholtz equation with both Cauchy and Dirichlet boundary conditions. In this paper, we introduce an expression 1/(1+α2) ; α ∈ R, where α is the regularization parameter, which is multiplied by w(x; 1) and then added to the Cauchy and Dirichlet boundary conditions of the Helmholtz equation. This regularization parameter overcomes the shortcomings in the Q-BVM to account for the stability at α = 0 and extend it to the rest of values of R.
Item Type: | Article |
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Subjects: | Middle Asian Archive > Computer Science |
Depositing User: | Managing Editor |
Date Deposited: | 19 May 2023 07:12 |
Last Modified: | 30 Jul 2025 05:21 |
URI: | http://peerreview.go2articles.com/id/eprint/498 |