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British Journal of Mathematics & Computer Science

British Journal of Mathematics & Computer Science, ISSN: 2231-0851,Vol.: 22, Issue.: 2

Original-research-article

On the Notes of Quasi-Boundary Value Method for Solving Cauchy-Dirichlet Problem of the Helmholtz Equation

 

Benedict Barnes1 , F. O. Boateng2, S. K. Amponsah3 and E. Osei-Frimpong4
1,3,4Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
2Department of Interdisciplinary Studies, University of Education, Winneba, Kumasi, Ghana.

 

Abstracts

 

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.

 

Keywords :

Expresion 1/(1+ α2) ; Q-BVM; ill-posed Helmholtz equation.

 

Full Article - PDF    Page 1-10    Article Metrics

 

DOI : 10.9734/BJMCS/2017/32727

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