skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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.

Authors:
; ;  [1]
  1. 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.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
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; THREE-DIMENSIONAL CALCULATIONS; TIME DEPENDENCE; WAVE EQUATIONS

Citation Formats

Litynskyy, S. V., Muzychuk, Yu. A., and Muzychuk, A. O. Combination of the Laguerre Transform with the Boundary-element Method for the Solution of Integral Equations with Retarded Kernel. United States: N. p., 2019. Web. doi:10.1007/S10958-018-4100-X.
Litynskyy, S. V., Muzychuk, Yu. A., & Muzychuk, A. O. Combination of the Laguerre Transform with the Boundary-element Method for the Solution of Integral Equations with Retarded Kernel. United States. doi:10.1007/S10958-018-4100-X.
Litynskyy, S. V., Muzychuk, Yu. A., and Muzychuk, A. O. Tue . "Combination of the Laguerre Transform with the Boundary-element Method for the Solution of Integral Equations with Retarded Kernel". United States. doi:10.1007/S10958-018-4100-X.
@article{osti_22773578,
title = {Combination of the Laguerre Transform with the Boundary-element 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 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.},
doi = {10.1007/S10958-018-4100-X},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 1,
volume = 236,
place = {United States},
year = {2019},
month = {1}
}