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

• Autorzy: Litynskyy S. , Muzychuk Y. , Muzychuk A.

Identyfikatory

DOI

10.1515/ama-2016-0044

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

boundary integral equation; time-domain boundary integral equation; wave equation; Sobolev spaces; generalized solution; retarded surface potentials; Laguerre transform; boundary elements method

PL

metoda elementów brzegowych; MEB; przestrzenie Sobolewa; transformata Laguerre'a; równanie falowe

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2016
• Tom: Vol. 10, no. 4
• Strony: 285--290
• Opis fizyczny: Bibliogr. 27 poz., tab., wykr.

Twórcy

autor

Litynskyy S.

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

autor

Muzychuk Y.

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

autor

Muzychuk A.

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

Bibliografia

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Uwagi

EN

The work has been accomplished under the research project at Ivan Franko National University of Lviv (State budgetary program "Numerical solution of linear and nonlinear problems of computational mathematics'' # 0110U003150).

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)