Implicit difference methods for infinite systems of hyperbolic functional differential equations

• Autorzy: Szafrańska A.
• Języki publikacji: EN

Abstrakty

EN

The paper deal with classical solutions of initial boundary value problems for infinite systems of nonlinear differential functional equations. Two types of difference schemes are constructed. First we show that solutions of our differential problem can be approximated by solutions of infinite difference functional schemes. In the second part of the paper we proof that solutions of finite difference systems approximate the solutions of aur differential problem. We give a complete convergence analysis for both types of difference methods. We adopt nonlinear estimates of the Perron type for given functions with respect to the functional variable. The proof of the stability is based on the comparison technique. Numerical examples are presented.

Słowa kluczowe

EN

initial boundary value problems; difference functional equations; difference methods; stability and convergence; interpolating operators; nonlinear estimates of Perron type

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2010
• Tom: Vol. 50, [Z] 1
• Strony: 73--86
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Szafrańska A.

• Gdansk University of Technology Gabriela Narutowicza 11-12, Gdansk, Poland,

Bibliografia

• [1] P. Brandi, Z. Kamont, A. Salvadori, Difference methods for nonlinear first order partial differential equations with mixed initial boundary conditions, Math. Balkanica 10, no. 2-3 (1996), 249-269.
• [2] T. Człapiński, The mixed problem for an infinite system of first order functional differential equations, Univ. Iagel. Acta Math. no. 39 (2001), 207-228.
• [3] Z. Kamont, Finite difference approximations for first order partial differential functional equations, Ukr. Math. J. 46 (1994), 985-996.
• [4] Z. Kamont, Stability of difference-functional equations and applications, Recent advances in numerical methods and applications, II (Sofia, 1998), 4051, World Sci. Publ., River Edge, NJ (1999).
• [5] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Dordrecht: Kluver Acad. Publ. 1999.
• [6] Z. Kamont, Infinite systems of hyperbolic functional differential inequalities, Nonlinear Analysis 51 (2002), 1429-1445.
• [7] Z. Kamont, K. Prządka, Difference methods for first order partial differential functional equations with initial - boundary condtions, J. Vycisl. Mat. i Math. Fis. 31 (1991), 1476-1488.
• [8] J. Szarski, Infinite systems of first-order partial-differential functional inequalities, General Inequalities, 2 (Proc. Second Internat. Conf., Oberwolfach, 1978), pp. 121126, Birkhäuser, Basel-Boston, Mass., 1980.
• [9] J. Szarski, Comparison theorems for infinite systems of differential-functional equations and strongly coupled infinite systems of first-order partial differential equation, Rocky Mountain J. Math. 10, no. 1 (1980), 239-246.