- Tytuł:
- A finite difference method for nonlinear parabolic-elliptic systems of second-order partial differential equations
- Autorzy:
-
Malec, M.
Sapa, L. - Powiązania:
- https://bibliotekanauki.pl/articles/255499.pdf
- Data publikacji:
- 2007
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
partial differential equation
parabolic-elliptic system
finite difference method
finite difference scheme
consistence
convergence
stability
error estimate
uniqueness - Opis:
- This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in R1+n. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.
- Źródło:
-
Opuscula Mathematica; 2007, 27, 2; 259-289
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł