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Abstrakty
We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.
Czasopismo
Rocznik
Tom
Strony
109--130
Opis fizyczny
Bibliogr. 8 poz.
Twórcy
autor
- University of Gdańsk, Institute of Mathematics, Wit Stwosz Street 57, 80-952 Gdańsk, Poland, zkamont@math.univ.gda.pl
Bibliografia
- [1] Brunner H.: The numerical treatment of ordinary and partial Volterra integro-differential equations. Proc. First Internat. Colloquium on Numerical Anal., Plovdiv, 17-23 August 1992; Bainov D., Covachev V. (Eds), 13-26, VSP Utrecht, Tokyo, 1993.
- [2] Godlewski E., Raviart P.: Numerical Approximation of Hyperbolic Systems of Conservation Laws. Berlin, Heidelberg, New York, Tokyo, Springer 1996.
- [3] Kamont Z.: Hyperbolic Functional Differential Inequalities and Applications. Dordrecht, Boston, London, Kluwer Acad. Publ. 1999.
- [4] Leszczyński H.: Convergence of one-step difference methods for nonlinear parabolic differential — functiolanl systems with initial boundary conditions of the Dirichlet type. Ann. Soc. Polon. Math., Comm. Math. 30(1990), 357-375.
- [5] Malec M., Schiafiano A.: Metode aux differences finies pour une equation non-lineaire differentielle finctionnelle du type parabolique avec une condition initiale de Cauchy. Boll. Un. Mat. Ital. B (7), 1(1987), 99-109.
- [6] Reinhardt H.J.: Analysis of Approxiamtion Methods for Differential and Integral Equations. New York, Springer-Verlag 1985.
- [7] Pao C.V.: Finite difference reaction-diffusion systems with coupled boundary conditions and time delay. J. Math. Anal. Appl. 272(2002), 407-434.
- [8] Voigt W.: On finite-difference methods for parabolic functional-differential equations on unbounded domains. Numerical Methods and Applications, 559-567, Sofia, Publ. House Bulg. Acad. Sci.1989.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0001-0022