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Title: Numerical solution of a generalized boundary value problem for the modified Helmholtz equation in two dimensions
Authors: Ivanyshyn Yaman, Olha
Özdemir, Gazi
Keywords: Generalized impedance boundary condition
Modified Helmholtz equation
Boundary integral equations
Hyper-singular kernels
Issue Date: 2021
Publisher: Elsevier
Abstract: We propose numerical schemes for solving the boundary value problem for the modified Helmholtz equation and generalized impedance boundary condition. The approaches are based on the reduction of the problem to the boundary integral equation with a hyper-singular kernel. In the first scheme the hyper-singular integral operator is treated by splitting off the singularity technique whereas in the second scheme the idea of numerical differentiation is employed. The solvability of the boundary integral equation and convergence of the first method are established. Exponential convergence for analytic data is exhibited by numerical examples. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.Y. All rights reserved.
ISSN: 0378-4754
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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