Comparison of explicit and implicit difference methods for quasilinear functional differential equations

W. Czernous, and Z. Kamont. "Comparison of explicit and implicit difference methods for quasilinear functional differential equations." Applicationes Mathematicae 38.3 (2011): 315-340. <http://eudml.org/doc/279939>.

@article{W2011,
abstract = { 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.:wn },
author = {W. Czernous, Z. Kamont},
journal = {Applicationes Mathematicae},
keywords = {differential and difference inequalities; stability; convergence; interpolating operators; first order partial functional differential equations; parabolic functional differential problems; difference methods; quasilinear functional differential equations; initial boundary value problems; error estimates; stability},
language = {eng},
number = {3},
pages = {315-340},
title = {Comparison of explicit and implicit difference methods for quasilinear functional differential equations},
url = {http://eudml.org/doc/279939},
volume = {38},
year = {2011},
}

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
VL - 38
IS - 3
SP - 315
EP - 340
AB - 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.:wn
LA - eng
KW - differential and difference inequalities; stability; convergence; interpolating operators; first order partial functional differential equations; parabolic functional differential problems; difference methods; quasilinear functional differential equations; initial boundary value problems; error estimates; stability
UR - http://eudml.org/doc/279939
ER -