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Abstrakty
The paper deals with the difference inequalities generated by initial boundary value problems for hyperbolic nonlinear differential functional systems. We apply this result to investigate the stability of constructed difference schemes. The proof of the convergence of the difference method is based on the comparison technique, and the result for difference functional inequalities is used. Numerical examples are presented.
Czasopismo
Rocznik
Tom
Strony
405--423
Opis fizyczny
Bibliogr. 19 poz., tab.
Twórcy
autor
- Gdansk University of Technology Department of Applied Physics and Mathematics ul. Gabriela Narutowicza 11-12, 80-952 Gdansk, Poland
Bibliografia
- [1] P. Brandi, Z. Kamont, A. Salvadori, Approximate solutions of mixed problems for first order partial differential-functional equations, Atti. Sem. Mat. Fis. Univ. Modena 39 (1991) 1, 277–302.
- [2] P. Brandi, Z. Kamont, A. Salvadori, Differential and differential-difference inequalities related to mixed problems for first order partial differential-functional equations, Atti. Sem. Mat. Fis. Univ. Modena 39 (1991) 1, 255–276.
- [3] E. Godlewski, P.-A. Reviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer, New York, NY, USA, 1996.
- [4] D. Gottlieb, E. Tadmor, The CFL condition for spectral approximations to hyperbolic initial-boundary value problems, Math. of Computat. 56 (1991), 565–588.
- [5] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kluver Acad. Publ., Dordrecht, 1999.
- [6] A. Kepczynska, Implicit difference functional inequalities and applications, Math. Balk. 20 (2006) 2, 167–184.
- [7] Z. Kowalski, A difference method for the non-linear partial differential equations of the first order, Ann. Polon. Math. 18 (1966), 235–242.
- [8] M. Malec, Sur une famille bi-paramétrique de schémas des différences finies pour l’équation parabolique sans dérivées mixtes, Ann. Polon. Math. 31 (1975), 47–54.
- [9] M. Malec, Sur une famille bi-paramétrique des schémas des différences pour les systems paraboliques, Bull. Acad. Polon. Sci. Sèr. Sci. Math. Astronom. Phys. 23 (1975) 8, 871–875.
- [10] M. Malec, Sur une famille biparamétrique de schémas des différences finies pour un systéme d’équations paraboliques aux dérivées mixtes et avec des conditions aux limites du type de Neumann, Ann. Polon. Math. 32 (1976), 33–42.
- [11] M. Malec, M. Rosati, A convergent scheme for nonlinear systems of differential functional equations of parabolic type, Rendiconti di Matematica. Serie VII 3 (1983) 2, 211–227.
- [12] M. Malec, C. Maczka, W. Voigt, Weak difference-functional inequalities and their application to the difference analogue of non-linear parabolic differential-functional equations, Beiträge zur Numerischen Mathematik 11 (1983), 69–79.
- [13] M. Malec, M. Rosati, Weak monotonicity for nonlinear systems of functional-finite difference inequalities of parabolic type, Rendiconti di Matematica. Serie VII 3 (1983) 1, 157–170.
- [14] M. Malec, A. Schiaffino, Méthode aux diffÞerences finies pour une équation non-linéaire differentielle fonctionnelle du type parabolique avec une condition initiale de Cauchy, Bollettino della Unione Matemática Italiana. Serie VII. B 1 (1987) 1, 99–109.
- [15] K.W. Morton, D.F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, 1994.
- [16] A. Plis, On difference inequalities corresponding to partial differential inequalities of the first order, Ann. Polon. Math. 20 (1968), 179–181.
- [17] K. Przadka, Difference methods for non-linear partial differential-functional equations of first order, Math. Nachr. 138 (1988), 105–123.
- [18] A.A. Samarskii, The theory of difference schemes, vol. 249 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2001.
- [19] A.A. Samarskii, P.P. Matus, P.N. Vabishchevich, Difference Schemes with Operator Factors, vol. 546 of Mathematics and Its Applications, Kluver Acad. Publ., Dordrecht, The Netherlands, 2002.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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