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Abstrakty
We prove a comparison theorem for an ODE and DAE system which arises from the method of lines. Under a Perron comparison condition on the functional dependence and a specific Lipschitz and (W+) condition on the classical argument, we obtain strong uniqueness criteria.
Wydawca
Czasopismo
Rocznik
Tom
Strony
137--154
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland, hleszcz@mat.ug.edu.pl
Bibliografia
- [1] K. E. Brenan, S. L. Campbell and L. R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia, 1995.
- [2] S. Burys, Finite difference method for non-linear parabolic equation in unbounded region, Univ. Iagellon. Ada Math. 24 (1984), 159-176.
- [3] I. Gyori, The method of lines for the solutions of some nonlinear partial differential equations, Comput. Math. Appl. 15 (1988), 635-648.
- [4] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 1999.
- [5] H.-O. Kreiss and H. U. Busenhart, Time-dependent Partial Differential Equations and their Numerical Solution, Birkhauser, Basel, 2001.
- [6] R. Kress, Numerical Analysis, Springer-Verlag, New York, 1998.
- [7] M. Malec and A. Schaffiano, Methode aux differences linies pour une l'equation non lineaire differentielle fonctionelle du type parabolic avec une condition initiale de Cauchy, Boll. Un. Mat. Ital. B(l) 7 (1987), 99-109.
- [8] W. E. Schiesser, The Numerical Method of Lines, Acad. Press, San Diego, 1991.
- [9] A. Voigt, The method of lines for nonlinear parabolic differential equations with mixed derivatives, Numer. Math. 32 (1979), 197-207.
- [10] W. Walter, Ordinary Differential Equations, Springer-Verlag, New York, 1998.
- [11] B. Zubik-Kowal, The method of lines for parabolic differential functional equations, IMA Journ. Numer. Anal. 17 (1997), 103-123.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-LOD7-0033-0019