Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
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.
Czasopismo
Rocznik
Tom
Strony
85--96
Opis fizyczny
Bibliogr. 5 poz.
Twórcy
autor
- Uniwersytet Gdański, Instytut Matematyki, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland, dana@math.univ.gda.pl
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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0005-0067