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Combination of the Laguerre Transform with the Boundary-element Method for the Solution of Integral Equations with Retarded Kernel

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We apply the Laguerre transform with respect to time to a time-dependent boundary-value integral equation encountered in the solution of three-dimensional Dirichlet initial-boundary-value problems for the homogeneous wave equation with homogeneous initial conditions by using the retarded potential of single layer. The obtained system of boundary integral equations is reduced to a sequence of Fredholm integral equations of the first kind that differ solely by the recursively dependent right-hand sides. To find their numerical solution, we use the boundary-element method. We establish an asymptotic estimate of the error of numerical solution and present the results of numerical simulations aimed at finding the solutions of retarded-potential integral equations for model examples.

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Authors and Affiliations

  1. Ivan Franko Lviv National University, Lviv, Ukraine

    S. V. Litynskyy, Yu. А. Muzychuk & А. О. Muzychuk

Authors
  1. S. V. Litynskyy
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  2. Yu. А. Muzychuk
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  3. А. О. Muzychuk
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 59, No. 3, pp. 89–101, July–September, 2016.

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Litynskyy, S.V., Muzychuk, Y.А. & Muzychuk, А.О. Combination of the Laguerre Transform with the Boundary-element Method for the Solution of Integral Equations with Retarded Kernel. J Math Sci 236, 98–114 (2019). https://doi.org/10.1007/s10958-018-4100-x

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