Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Access Right: Closed AccessSubject: search.filters.subject.Boundary integral equations

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  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Numerical Solution of a Generalized Boundary Value Problem for the Modified Helmholtz Equation in Two Dimensions
    (Elsevier, 2021) Ivanyshyn Yaman, Olha; Özdemir, Gazi
    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.
  • Article
    Citation - WoS: 3
    On the Non-Linear Integral Equation Approaches for the Boundary Reconstruction in Double-Connected Planar Domains
    (Ivan Franko National University of Lviv,, 2016) Chapko, R. S.; Yaman, Olha Ivanyshyn; Kanafotskyi, T. S.
    We consider the reconstruction of an interior curve from the given Cauchy data of a harmonic function on the exterior boundary of the planar domain. With the help of Green's function and potential theory the non-linear boundary reconstruction problem is reduced to the system of non-linear boundary integral equations. The three iterative algorithms are developed for its numerical solution. We find the Frechet derivatives for the corresponding operators and show unique solviability of the linearized systems. Full discretization of the systems is realized by a trigonometric quadrature method. Due to the inherited ill-possedness in the obtained system of linear equations we apply the Tikhonov regularization. The numerical results show that the proposed methods give a good accuracy of reconstructions with an economical computational cost.