Research Articles >
College of Science >
Please use this identifier to cite or link to this item:
|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.
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
(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|
|Appears in Collections:||College of Science|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.