The finite difference scheme for the solution of one quasilinear equation

• Autorzy: Ciegis R. , Ciegis R. , Rate P.
• Języki publikacji: EN

Abstrakty

EN

In this paper we are interested in the solution of one-dimensional quasi-linear diffusion-reaction equation. The nonlinear reaction term includes the first derivative in space of the solution. We use the finite difference method to discretize this problem. The modification of a general methodology for investigation of difference schemes approximating non-stationary differential equations is used and the results for the stability and convergence of the numerical solution are proved. The convergence of the discrete derivative of the solution is proved in the maximum norm.

Słowa kluczowe

EN

quasilinear parabolic equation; finite difference schemes; convergence

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 3
• Strony: 723--732
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Ciegis R.

• Vilnius Gediminas Technical University Sauletekio Str. 11 2054 Vilnius, Lithuania

autor

Ciegis R.

• Vilnius University, Kaunas Humanitarian Faculty Muitines Str. 8 3000 Kaunas, Lithuania

autor

Rate P.

• Vytautas Magnus University Vileikos 8 3000 Kaunas, Lithuania

Bibliografia

• [1] Raim. Čiegis, Rem. Čiegis, and M. Meilūnas, On a general method for investigation of finite difference schemes, Lithuanian. Math. J. 36 (1996), 224-241.
• [2] Raim. Čiegis, Rem. Čiegis, and O. Štikoniene, On extension of one method for investigation of nonlinear difference schemes, Lithuanian. Math. J. 37 (1997), 119-128.
• [3] K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Computational Differential Equations, University Press, Cambridge 1996.
• [4] A. Friedman, Mathematics in Industrial Problems, Part. 3, IMA Math. Appl., Vol. 31, Springer-Verlag, New-York 1990.
• [5] Q. He, L. Kang and D. J. Evans, Convergence and stability of the finite difference scheme for nonlinear parabolic systems with time delay, Numer. Algorithms 16 (1997), 129-153.
• [6] J. K. Hale, Dynamics of a scalar parabolic equation, CWI Quarterly 12 (1999), 239-314.
• [7] F. Ivanauskas and T. Meskauskas, On convergence and stability of difference schemes for derivative nonlinear Shrodinger and other evolution equations, Lithuanian Math. J. 36 (1996), 10-20.
• [8] P. J. Roach, Computational Fluid Dynamics, Hermosa Publishers, Albuquerque 1976.
• [9] A. A. Samarskii, The Theory of Difference Schemes, Nauka, Moscow 1988 (in Russian).
• [10] A. A. Samarskii and V. B. Andreev, Difference Methods for Elliptic Equations, Nauka, Moscow 1976 (in Russian).