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

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  • Ivanyshyn Yaman, Olha
  • Özdemir, Gazi

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.

Suggested Citation

  • Ivanyshyn Yaman, Olha & Özdemir, Gazi, 2021. "Numerical solution of a generalized boundary value problem for the modified Helmholtz equation in two dimensions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 181-191.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:181-191
    DOI: 10.1016/j.matcom.2021.05.013
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    References listed on IDEAS

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    1. Bin-Mohsin, B. & Lesnic, D., 2012. "Determination of inner boundaries in modified Helmholtz inverse geometric problems using the method of fundamental solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1445-1458.
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