Combination of the Laguerre Transform with the Boundaryelement Method for the Solution of Integral Equations with Retarded Kernel
Abstract
We apply the Laguerre transform with respect to time to a timedependent boundaryvalue integral equation encountered in the solution of threedimensional Dirichlet initialboundaryvalue 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 righthand sides. To find their numerical solution, we use the boundaryelement 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 retardedpotential integral equations for model examples.
 Authors:

 Ivan Franko Lviv National University (Ukraine)
 Publication Date:
 OSTI Identifier:
 22773578
 Resource Type:
 Journal Article
 Journal Name:
 Journal of Mathematical Sciences
 Additional Journal Information:
 Journal Volume: 236; Journal Issue: 1; Other Information: Copyright (c) 2019 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springerny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 10723374
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; BOUNDARY ELEMENT METHOD; COMPUTERIZED SIMULATION; DIRICHLET PROBLEM; ERRORS; FREDHOLM EQUATION; KERNELS; LAYERS; THREEDIMENSIONAL CALCULATIONS; TIME DEPENDENCE; WAVE EQUATIONS
Citation Formats
Litynskyy, S. V., Muzychuk, Yu. A., and Muzychuk, A. O. Combination of the Laguerre Transform with the Boundaryelement Method for the Solution of Integral Equations with Retarded Kernel. United States: N. p., 2019.
Web. doi:10.1007/S109580184100X.
Litynskyy, S. V., Muzychuk, Yu. A., & Muzychuk, A. O. Combination of the Laguerre Transform with the Boundaryelement Method for the Solution of Integral Equations with Retarded Kernel. United States. doi:10.1007/S109580184100X.
Litynskyy, S. V., Muzychuk, Yu. A., and Muzychuk, A. O. Tue .
"Combination of the Laguerre Transform with the Boundaryelement Method for the Solution of Integral Equations with Retarded Kernel". United States. doi:10.1007/S109580184100X.
@article{osti_22773578,
title = {Combination of the Laguerre Transform with the Boundaryelement Method for the Solution of Integral Equations with Retarded Kernel},
author = {Litynskyy, S. V. and Muzychuk, Yu. A. and Muzychuk, A. O.},
abstractNote = {We apply the Laguerre transform with respect to time to a timedependent boundaryvalue integral equation encountered in the solution of threedimensional Dirichlet initialboundaryvalue 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 righthand sides. To find their numerical solution, we use the boundaryelement 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 retardedpotential integral equations for model examples.},
doi = {10.1007/S109580184100X},
journal = {Journal of Mathematical Sciences},
issn = {10723374},
number = 1,
volume = 236,
place = {United States},
year = {2019},
month = {1}
}