The Sturm-Liouville eigenvalue problem - a numerical solution using the control volume method

• Autorzy: Siedlecki J. , Ciesielski M , Błaszczyk T.

Identyfikatory

DOI

10.17512/jamcm.2016.2.14

• Języki publikacji: EN

Abstrakty

EN

The solution of the 1D Sturm-Liouville problem using the Control Volume Method is discussed. The second order linear differential equation with homogeneous boundary conditions is discretized and converted to the system of linear algebraic equations. The matrix associated with this system is tridiagonal and eigenvalues of this system are an approximation of the real eigenvalues of the boundary value problem. The numerical results of the eigenvalues for various cases and the experimental rate of convergence are presented.

Słowa kluczowe

EN

Sturm-Liouville problem; eigenvalues; numerical methods; Control Volume Method

PL

problem Sturm-Liouville; wartości własne; metody numeryczne; metoda kontroli głośności

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 2
• Strony: 127--136
• Opis fizyczny: Bibliogr. 14 poz., tab.

Twórcy

autor

Siedlecki J.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Ciesielski M

• Institute of Computer and Information Sciences Czestochowa University of Technology, Częstochowa, Poland

autor

Błaszczyk T.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

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• [12] Akulenko L.D., Nesterov S.V., High-Precision Methods in Eigenvalue Problems and Their Applications (series: Differential and Integral Equations and Their Applications), Chapman and Hall/CRC, 2004.
• [13] Ciesielski M., Blaszczyk T., Numerical solution of non-homogenous fractional oscillator equation in integral form, Journal of Theoretical and Applied Mechanics 2015, 53 (4), 959-968.
• [14] Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P., Numerical Recipes: The Art of Scientific Computing (3rd ed.), Cambridge University Press, New York 2007.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.