Mathematics / Matematik

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

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Publisher: search.filters.publisher.Ivan Franko National University of Lviv,Scopus Q: search.filters.scopusQuartile.N/A

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  • 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.
  • Article
    Citation - WoS: 1
    On the Non-Linear Integral Equation Method for the Reconstruction of an Inclusion in the Elastic Body
    (Ivan Franko National University of Lviv,, 2019) Chapko, R. S.; Yaman, Olha Ivanyshyn; Vavrychuk, V. G.
    We apply the non-linear integral equation approach based on elastic potentials for determining the shape of a bounded object in the elastostatic two-dimensional domain from given Cauchy data on its boundary. The iterative algorithm is developed for the numerical solution of obtained integral equations. We find the Frechet derivative for the corresponding operator and show unique solviability of the linearized system. Full discretization of the system is realized by a trigonometric quadrature method. Due to the inherited ill-possedness in the system of linear equations we apply the Tikhonov regularization. The numerical results show that the proposed method gives a good accuracy of reconstructions with an economical computational cost.