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

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 o...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2019, Vol.236 (1), p.98-114
Main Authors: Litynskyy, S. V., Muzychuk, Yu. А., Muzychuk, А. О.
Format: Article
Language:English
Subjects:
Asymptotic methods
ASYMPTOTIC SOLUTIONS
BOUNDARY ELEMENT METHOD
Boundary integral method
Boundary value problems
Computer simulation
COMPUTERIZED SIMULATION
DIRICHLET PROBLEM
ERRORS
FREDHOLM EQUATION
Fredholm equations
Initial conditions
Integral equations
KERNELS
LAYERS
MATHEMATICAL METHODS AND COMPUTING
Mathematical models
Mathematics
Mathematics and Statistics
THREE-DIMENSIONAL CALCULATIONS
TIME DEPENDENCE
WAVE EQUATIONS
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-4100-x