<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We consider a numerical solution of the initial-boundary value problem for the homogeneous wave equation with the Neumann condition using the retarded double layer potential. For solving an equivalent time-dependent integral equation we combine the Laguerre transform (LT) in the time domain with the boundary elements method. After LT we obtain a sequence of boundary integral equations with the same integral operator and functions in right-hand side which are determined recurrently. An error analysis for the numerical solution in accordance with the parameter of boundary discretization is performed. The proposed approach is demonstrated on the numerical solution of the model problem in unbounded three-dimensional spatial domain.</p></abstract>

We consider a numerical solution of the initial-boundary value problem for the homogeneous wave equation with the Neumann condition using the retarded double layer potential. For solving an equivalent time-dependent integral equation we combine the Laguerre transform (LT) in the time domain with the boundary elements method. After LT we obtain a sequence of boundary integral equations with the same integral operator and functions in right-hand side which are determined recurrently. An error analysis for the numerical solution in accordance with the parameter of boundary discretization is performed. The proposed approach is demonstrated on the numerical solution of the model problem in unbounded three-dimensional spatial domain.

On the Numerical Solution of the Initial-Boundary Value Problem with Neumann Condition for the Wave Equation by the Use of the Laguerre Transform and Boundary Elements Method

Applied Mathematics and Informatics, Programming Department, Ivan Franko National University of Lviv, Universytetska 1, Lviv,

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We consider a numerical solution of the initial-boundary value problem for the homogeneous wave equation with the Neumann condition using the retarded double...

On the Numerical Solution of the Initial-Boundary Value Problem with Neumann Condition for the Wave Equation by the Use of the Laguerre Transform and Boundary Elements Method

Published Online: Dec 28, 2016

Page range: 285 - 290

Received: Jun 29, 2016

Accepted: Dec 01, 2016

DOI: https://doi.org/10.1515/ama-2016-0044

Keywords
Boundary Integral Equation, Time-Domain Boundary Integral Equation, Wave Equation, Sobolev Spaces, Generalized Solution, Retarded Surface Potentials, Laguerre Transform, Boundary Elements Method

© 2016 Bialystok University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the Numerical Solution of the Initial-Boundary Value Problem with Neumann Condition for the Wave Equation by the Use of the Laguerre Transform and Boundary Elements Method

Published Online: Dec 28, 2016

Page range: 285 - 290

Received: Jun 29, 2016

Accepted: Dec 01, 2016

DOI: https://doi.org/10.1515/ama-2016-0044

KeywordsBoundary Integral Equation, Time-Domain Boundary Integral Equation, Wave Equation, Sobolev Spaces, Generalized Solution, Retarded Surface Potentials, Laguerre Transform, Boundary Elements Method

© 2016 Bialystok University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Boundary Integral Equation, Time-Domain Boundary Integral Equation, Wave Equation, Sobolev Spaces, Generalized Solution, Retarded Surface Potentials, Laguerre Transform, Boundary Elements Method