Difference methods for infinite systems of quasilinear parabolic functional differential equations

• Autorzy: Jaruszewska-Walczak D.
• Języki publikacji: EN

Abstrakty

EN

Classical solutions of initial boundary value problems for infinite systems of quasilinear parabolic differential functional equations are considered. Two type of difference schemes are constructed. We prove that solutions of infinite difference schemes approximate solutions of our differential functional problem. In the second part of the paper we show that solutions of infinite differential functional systems can be approximated by solutions of difference systems with initial boundary conditions and the systems are finite. A complete convergence analysis for the methods is presented. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given functions.

Słowa kluczowe

EN

initial boundary value problems; parabolic functions

PL

zagadnienie brzegowe; równanie paraboliczne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 1
• Strony: 213--230
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Jaruszewska-Walczak D.

• Institute of Mathematics University of Gdańsk Wita Stwosza 57 80-952 Gdańsk, Poland,

Bibliografia

• [1] S. Brzychczy, Infinite Systems of Parabolic Differential-Functional Equations, AGH University of Science and Technology Press, Cracow, 2006.
• [2] R. Ciarski, Stability of difference equations generated by parabolic differential functional equations, Demonstratio Math. 38 (2005), 101-117.
• [3] D. Jaruszewska-Walczak, Comparison theorems for infinite systems of parabolic functional-differential equations, Ann. Polon. Math. 77 (2001), 261-270.
• [4] Z. Kamont, H. Leszczyński, Stability of difference equations generated by parabolic differential functional problems, Rend. Mat. Appl. (7) 16 (1996), 265-287.
• [5] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 1999.
• [6] M. Malec, Sur une méthode des différences finies pour équation non linéaire intégro différentielle à argument retardé (French), Bull. Acad. Polon. Sci., Ser. Sci. Math. Astr. Phys. 26 (1978), 501-517.
• [7] M. Malec, A. Schatiano, Méthode aux différences finies pour une equation non-linéair e différentielle fonctionelle du type parabolique avec une condition initiale de Cauchy (French), Boll. Un. Mat. Ital. (7) 1 (1987), 99-109.
• [8] J. Szarski, Comparison theorem for infinite systems of parabolic differential-functional equations and strongly coupled infinite systems of parabolic equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys. 27 (1979), 839-846.
• [9] J. Szarski, Infinite systems of parabolic differential functional inequalities, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys. 28 (1980), 477-481