Comparison of explicit and implicit difference methods for quasilinear functional differential equations
Applicationes Mathematicae, Tome 38 (2011) no. 3, pp. 315-340
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We give a theorem on error estimates of approximate solutions for explicit and implicit difference functional equations with unknown functions of several variables. We apply this general result to investigate the stability of difference methods for quasilinear functional differential equations with initial boundary condition of Dirichlet type. We consider first order partial functional differential equations and parabolic functional differential problems. We compare the properties of explicit and implicit difference methods. We use a comparison technique with nonlinear estimates of Perron type for given functions with respect to the functional variables.
DOI :
10.4064/am38-3-4
Keywords:
theorem error estimates approximate solutions explicit implicit difference functional equations unknown functions several variables apply general result investigate stability difference methods quasilinear functional differential equations initial boundary condition dirichlet type consider first order partial functional differential equations parabolic functional differential problems compare properties explicit implicit difference methods comparison technique nonlinear estimates perron type given functions respect functional variables
Affiliations des auteurs :
W. Czernous 1 ; Z. Kamont 1
@article{10_4064_am38_3_4,
author = {W. Czernous and Z. Kamont},
title = {Comparison of explicit and implicit difference methods for quasilinear functional differential equations},
journal = {Applicationes Mathematicae},
pages = {315--340},
year = {2011},
volume = {38},
number = {3},
doi = {10.4064/am38-3-4},
zbl = {1223.65067},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am38-3-4/}
}
TY - JOUR AU - W. Czernous AU - Z. Kamont TI - Comparison of explicit and implicit difference methods for quasilinear functional differential equations JO - Applicationes Mathematicae PY - 2011 SP - 315 EP - 340 VL - 38 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/am38-3-4/ DO - 10.4064/am38-3-4 LA - en ID - 10_4064_am38_3_4 ER -
%0 Journal Article %A W. Czernous %A Z. Kamont %T Comparison of explicit and implicit difference methods for quasilinear functional differential equations %J Applicationes Mathematicae %D 2011 %P 315-340 %V 38 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4064/am38-3-4/ %R 10.4064/am38-3-4 %G en %F 10_4064_am38_3_4
W. Czernous; Z. Kamont. Comparison of explicit and implicit difference methods for quasilinear functional differential equations. Applicationes Mathematicae, Tome 38 (2011) no. 3, pp. 315-340. doi: 10.4064/am38-3-4
Cité par Sources :