Numerical solution of a generalized boundary value problem for the modified Helmholtz equation in two dimensions

Olha Ivanyshyn Yaman and Gazi Özdemir

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 181-191

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.

Keywords: Generalized impedance boundary condition; Modified Helmholtz equation; Boundary integral equations; Hyper-singular kernels (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:181-191

DOI: 10.1016/j.matcom.2021.05.013

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