Exact difference schemes and schemes of higher order of approximation for convection-diffusion equation. I

• Autorzy: Lapinska-Chrzczonowicz M. , Matus P.

Identyfikatory

DOI

10.2478/v10065-012-0045-8

• Języki publikacji: EN

Abstrakty

EN

The initial-boundary value problem for a convection-diffusion equation [formula] is considered. The difference scheme, approximating this problem, is constructed. It is shown that for traveling wave solutions the scheme is exact (EDS). The monotonicity of the scheme is also taken into consideration. Presented numerical experiments illustrate the theoretical results investigated in the paper.

Słowa kluczowe

EN

convection-diffusion equation; initial-boundary value problem; traveling wave; EDS

• Wydawca: Wydawnictwo UMCS
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica
• Rocznik: 2013
• Tom: Vol. 13, no. 1
• Strony: 37--51
• Opis fizyczny: Bibliogr. 16 poz., rys., tab.

Twórcy

autor

Lapinska-Chrzczonowicz M.

• Institute of Mathematics and Computer Science, John Paul II Catholic University of Lublin, Al. Racławickie 14, 20-950 Lublin, Poland

autor

Matus P.

• Institute of Mathematics and Computer Science, John Paul II Catholic University of Lublin, Al. Racławickie 14, 20-950 Lublin, Poland
• Institute of Mathematics NAS of Belarus

Bibliografia

• [1] Samarskii A. A., Matus P. P., Vabishchevich P. N., Difference Schemes with Operator Factors, Kluwer Academic Publishers, Netherlands (2002).
• [2] Gavrilyuk I., Hermann M., Makarov V., Kutniv M. V., Exact and Truncated Difference Schemes for Boundary Value ODEs, Springer, Berlin (2011).
• [3] Micken R. E., Applications of Nonstandard Finite Difference Schemes,World Scientific Publishing, Singapore (2000).
• [4] Mickens R. E., Exact finite difference schemes for two-dimensional advection equations, Journal of Sound and Vibration 207(3) (1997): 426.
• [5] Paradzinska A., Matus P., High Accuracy Difference Schemes for Nonlinear Transfer Equation ∂u/∂t + u∂u/∂x = f(u), Mathematical Modelling and Analysis 12(4) (2007): 469.
• [6] Rucker S., Exact Finite Difference Scheme for an Advection–Reaction Equation, Journal of Difference Equations and Applications 9(11) (2003): 1007.
• [7] Matus P., Irkhin U., Lapinska-Chrzczonowicz M., Exact difference schemes for time-dependent problems, Computational Methods In Applied Mathematics 5(4) (2005): 422.
• [8] Matus P., Irkhin U., Lapinska-Chrzczonowicz M., Lemeshevsky S. V., On exact finite-difference schemes for hyperbolic and elliptic equations. Differentsial’nye, Uravneniya 43(7) (2007): 978.
• [9] Gilding B. H., Kersner R., Travelling Waves in Nonlinear Diffusion-Convection Reaction, Birkhauser Verlag, Berlin (2004).
• [10] Volpert A. I., Volpert V. A., Volpert V. A., Traveling Wave Solutions of Parabolic Systems, American Mathematical Society, Rhode Island (2000).
• [11] Samarskii A. A., The theory of difference schemes, Marcel Dekker Inc., New York - Basel (2001).
• [12] Smarskii A. A., Gulin A. W., Numerical methods, Nauka, Moscow (1989); (in Russian).
• [13] Matus P. P., Kirshtein A. A., Irkhin U. A., Exact difference schemes for the system of acoustic equations and analysis of Riemann problem, J. Numer. Appl. Math. 105(2) (2011): 83.
• [14] Lapinska-Chrzczonowicz M., Difference schemes of arbitrary order of accuracy for semilinear parabolic equations, Annales UMCS, Informatica 10(2) (2010): 93.
• [15] Hundsdorfer W., Verwer J. G., Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer, Berlin (2003).
• [16] Lemeshevsky S. V., Matus P. P., Yakubuk R. M., Two-layered higher-order difference schemes for the convection-diffusion equation, Doklady of The National Academy of Sciences of Belarus 56(2) 2012: 15.