Numerical method of bicharacteristics for quasilinear hyperbolic functional differential systems

• Autorzy: Kropielnicka K.
• Języki publikacji: EN

Abstrakty

EN

Classical solutions of mixed problems for first order partialfunctional differential systems in two independent variables areapproximated in the paper with solutions of a difference problemof the Euler type. The mesh for the approximate solutions isobtained by a numerical solving of equations of bicharacteristics.The convergence of explicit difference schemes is proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of the Perron type. Differential systems with deviated variables and differential integral systems can be obtained from a general model by specializing given operators.

Słowa kluczowe

EN

initial boundary value problems; bicharacteristics; interpolating operators

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2005
• Tom: Vol. 45, [Z] 1
• Strony: 91--109
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Kropielnicka K.

• Department of Mathematics Technical, University of Gdańsk,

Bibliografia

• [1] T. Czlapiński, On the mixed problem for quasilinear partial differential functional equations of the first order, Zeit. Anal. Anwend. 16 (1997), 463-478.
• [2] E. Godlewski, P. A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer, Berlin 1996.
• [3] D. Jaruszewska-Walczak, Z. Kamont, Difference methods for quasilinear hyperbolic differential functional systems on the Haar pyramid, Bull. Belg. Math. Soc. 10 (2003), 267-290.
• [4] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kluwer Acad. Publ., Dordrecht 1999.
• [5] K. M. Makhomedov, A. S. Kholodov, Mesh Characteristic Numerical Methods, Nauka, Moscow 1988 (Russian).
• [6] M. Malec, A. Schafiano, Méthode aux différences finies pour une équations non linéaire differentielle fonctionnelle du type parabolic avec une condition initiale de Cauchy, Bull. Un. Mat. Ital. 7 I-B (1987), 99-109.
• [7] M. Malec, Sur une méthode des différences finies pour équation non linéaire intégro différentielle á argument retardé, Bull. Acad, Polon. Sci., Ser. Sci. Math. Phys. Astr. 26 (1978), 501-517.
• [8] C. V. Pao, Numerical methods for systems of nonlinear parabolic equations with time delays, Journ. Math. Anal. Appl. 240 (1999), 249-279.
• [9] C. V. Pao, Numerical methods for nonlinear integro-parabolic equations of Fredholns type, Comput. Math. Appl. 41 (2001), 857-877.
• [10] J. Turo, Mixed problems for quasilinear hyperbolic systems, Nonl. Anal. TMA, 30 (1997), 2329-2340.