+91 8617752708

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


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
1Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
2Department of Interdisciplinary Studies, University of Education, Winneba, Kumasi, Ghana.

Article Information
(1) Jacek Dziok, Institute of Mathematics, University of Rzeszow, Poland.
(2) Andrej V. Plotnikov, Department of Applied and Calculus Mathematics and CAD, Odessa State Academy of Civil Engineering and Architecture, Ukraine.
(1) Abdullah Sonmezoglu, Bozok University, Turkey.
(2) Seval Catal, Dokuz Eyll University, Turkey.
Complete Peer review History: http://www.sciencedomain.org/review-history/19213


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

Review History    Comments

Our Contacts

Guest House Road, Street no - 1/6,
Hooghly, West Bengal,

+91 8617752708


Third Floor, 207 Regent Street
London, W1B 3HH,

+44 20-3031-1429