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Języki publikacji
Abstrakty
The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
29--46
Opis fizyczny
Bibliogr. 13 poz., tab.
Twórcy
autor
- University of Gdańsk, Institute of Mathematics, Wit Stwosz Street 57, 80-952 Gdańsk, rciarski@math.univ.gda.pl
Bibliografia
- [1] P. Brandi, Z. Kamont, A. Salvadori, Aproximate solutions of the mixed problems for first order partial differential-functional equations, Atti Sem. Mat. Fis. Univ. Modena 39 (1991), 277–302.
- [2] H. Bruner, The numerical treatment of ordinary and partial Volterra integro-differential equations, Proceed. First Internat. Colloq. on Numerical Anal., Plovdiv, 17–23 August 1992 (D. Bainov, V. Covacher., eds.), 13–26, Tokyo: VSP Ultrecht, 1993.
- [3] E. Godlewski, P. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer, Berlin, 1996.
- [4] W. Hakbusch, Extrapolation applied to certain discretization method solving the initial value problem for hyperbolic differential equations, Numer. Math. 28 (1977), 121–142.
- [5] Z. Kamont, K. Prządka, Difference methods for nonlinear partial differential equations of the first order, Ann. Polon. Math. 48 (1988), 227–246.
- [6] Z. Kamont, Hyperbolic functional differential inequalities and applications, Kluver Acad. Publ., Dordrecht, Boston, London, 1989.
- [7] Z. Kamont, Finite difference approximations for first order partial differential functional equations, Ukr. Math. Journ. 46 (1994), 985–996.
- [8] Z. Kamont, K. Prządka, Difference methods for first order partial differential functional equations with initial boundary conditions, Journ. Vycisl. Mat. i Mat. Fis. 31 (1991), 1476–1488.
- [9] Z. Kowalski, A difference method for nonlinear partial differential equations of the first order, Ann. Polon. Math. 18 (1960), 235–242.
- [10] Z. Kowalski, On the difference method for certain hyperbolic systems of non-linear partial differential equations of the first order, Bull. Acad. Polon. Sci., Ser. sci. math. astr.phys. 16 (1968) 4, 297–310.
- [11] K.M. Maghomedov, A.S. Holodov, Set-characteristics Numerical Methods, Moscow, 1988 (in Russian).
- [12] T. Meis, U. Marcowitz, Numerical Solutions of Partial Differential Equations, Acad. Press., New York, 1981.
- [13] K. Prządka, Difference methods for nonlinear partial differential functional equations of the first order, Math. Nachr. 138 (1988), 105–123.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH9-0002-0003