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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/11588

Title: On the Notes of Quasi-Boundary Value Method for Solving Cauchy-Dirichlet Problem of the Helmholtz Equation
Authors: Barnes, Benedict
Boateng, F. O.
Amponsah, S. K.
Osei-Frimpong, E.
Keywords: Q-BVM
ill-posed Helmholtz equation.
Issue Date: 2017
Publisher: British Journal of Mathematics & Computer Science
Citation: British Journal of Mathematics & Computer Science, 22(2): 1-10, 2017; Article no.BJMCS.32727
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 = 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+ 2) ; ∈ R, where 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 = 0 and extend it to the rest of values of R.
Description: An article published in British Journal of Mathematics & Computer Science, 22(2): 1-10, 2017; Article no.BJMCS.32727
URI: http://hdl.handle.net/123456789/11588
ISSN: 2231-0851
Appears in Collections:College of Science

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