The usage of Trefftz functions and Picard's iteration for solving different problems of a two-dimensional wave equation

• Autorzy: Krzyszkowska P. , Maciąg A. , Walaszczyk M.
• Języki publikacji: EN

Abstrakty

EN

The paper presents a method of solving two-dimensional wave equations which describe vibrations of the membrane with variable thickness and with damping. The differential operator is decomposed into two parts. The first one describes vibrations of the membrane with constant thickness without damping. The second contains the rest of the original operator and is treated as inhomogeneity for the first one. Picard’s iterations are used to calculate a successive approximation of the exact solution. Trefftz functions (wave polynomials) are used to solve the problem in each iteration. The presented examples show the usefulness of the method. The approach described in this paper can be used also for solving nonlinear problems for a wave equation.

Słowa kluczowe

EN

wave equation; Trefftz functions; Picard's iteration

PL

równanie falowe; funkcje Trefftza; iteracja Picarda

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 3
• Strony: 129--140
• Opis fizyczny: Bibliogr. 20 poz., rys., tab.

Twórcy

autor

Krzyszkowska P.

• Faculty of Mechatronics and Machine Design, Kielce University of Technology Kielce, Poland

autor

Maciąg A.

• Faculty of Management and Computer Modelling, Kielce University of Technology Kielce, Poland

autor

Walaszczyk M.

• Faculty of Mechatronics and Machine Design, Kielce University of Technology Kielce, Poland

Bibliografia

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