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Abstrakty
The paper deals with the initial boundary value problem for quasilinear first order partial differential functional equations. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional equations are presented. The convergence results are proved by means of consistency and stability arguments. Numerical example is given.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
557--571
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
- Institute of Mathematics, University of Gdansk, Wit Stwosz Street 57, 80-952 Gdańsk, Poland
Bibliografia
- [1] 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.) pp. 13-26. Tokyo: VSP Ultrecht, 1993.
- [2] E. Godlewski, P. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer, Berlin, 1996.
- [3] W. Hakbusch, Extrapolation applied to certain discretization method solving the initial value problem for hyperbolic differential equations, Numer. Math. 28 (1977), 121-142.
- [4] Z. Kamont, Finite difference approximations for first order partial differential functional equations, Ukrainian. Math. J. 46 (1994), 985-996.
- [5] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kluwer Acad. Publ., Dordrecht, Boston, London, 1999.
- [6] Z. Kamont and K. Prządka, Difference method for nonlinear partial differential equations of the first order, Ann. Polon. Math. 48 (1988), 227-246.
- [7] Z. Kamont, K. Prządka, Difference methods for first order partial differential functional equations with initial boundary condition, J. Comput. Math, and Math. Phys. 31 (1991), 1476-1488.
- [8] Z. Kowalski, A difference method for nonlinear partial differential equations of the first order, Ann. Polon. Math. 18 (1960), 235-242.
- [9] V. Lakshmikantham, D. Trigiante, Difference Equations with Applications to Numerical Analysis, Acad. Press., New York, 1988.
- [10] K. M. Maghomedov, A. S. Holodov, Set-characteristics Numerical Methods, Moscow, 1988 (in Russian).
- [11] T. Meis, U. Marcowitz, Numerical Solutions of Partial Differential Equations, Acad. Press., New York, 1981.
- [12] 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-PWA1-0044-0012