On the Notes of Quasi-Boundary Value Method for Solving Cauchy-Dirichlet Problem of the Helmholtz Equation
Journal Title: Journal of Advances in Mathematics and Computer Science - Year 2017, Vol 22, Issue 2
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.
Authors and Affiliations
Benedict Barnes, F. O. Boateng, S. K. Amponsah, E. Osei-Frimpong
Keywords
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