Difference methods for infinite systems of hyperbolic functional differential equations on the Haar pyramid

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

Abstrakty

EN

We consider the Cauchy problem for infinite system of differential functional equations ∂tzk(t, x) = fk(t, x, z, ∂xzk(t, x)), k mem N. In the paper we consider a general class of difference methods for this problem. We prove the convergence of methods under the assumptions that given functions satisfy the nonlinear estimates of the Perron type with respect to functional variables. The proof is based on functional difference inequalities. We constructed the Euler method as an example of difference method.

Słowa kluczowe

EN

initial problems; infinite systems of differential functional equations; difference functional inequalities; nonlinear estimates of Perron type

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2004
• Tom: Vol. 24, no. 1
• Strony: 85--96
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Jaruszewska-Walczak D.

• Uniwersytet Gdański, Instytut Matematyki, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland,

Bibliografia

• [1] Jaruszewska-Walczak D., Kamont Z.: Numerical methods for hyperbolic functional differential problems on the Haar pyramid. Computing 65 (2000), 45-72.
• [2] Kamont Z.: Iterative methods for hyperbolic differential-functional problems. Discuss. Math. 13 (1993), 93-117.
• [3] Kamont Z.: Infinite systems of hyperbolic functional differential inequalities. Nonlinear Anal. 51 (2002), 1429-1445.
• [4] Kowalski Z.: A difference method for certain hyperbolic systems of non-linear partial differential equations of the first order. Ann. Polon. Math. 19 (1967), 313-322.
• [5] Kowalski Z.: 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. Astronom. Phys. 16 (1968), 297-302.