A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Dirichlet's condition

Lucjan Sapa. "A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Dirichlet's condition." Annales Polonici Mathematici 93.2 (2008): 113-133. <http://eudml.org/doc/280775>.

@article{LucjanSapa2008,
abstract = {We deal with a finite difference method for a wide class of nonlinear, in particular strongly nonlinear or quasi-linear, second-order partial differential functional equations of parabolic type with Dirichlet's condition. The functional dependence is of the Volterra type and the right-hand sides of the equations satisfy nonlinear estimates of the generalized Perron type with respect to the functional variable. Under the assumptions adopted, quasi-linear equations are a special case of nonlinear equations. Quasi-linear equations are also treated separately. It is proved that our numerical methods are consistent, convergent and stable. Error estimates are given. The proofs are based on the comparison technique. Examples of physical applications and numerical experiments are presented.},
author = {Lucjan Sapa},
journal = {Annales Polonici Mathematici},
keywords = {nonlinear and quasi-linear differential functional equations of parabolic type; finite difference methods; stability; convergence; nonlinear estimates of the generalized Perron type; consistency; error estimates; numerical experiments},
language = {eng},
number = {2},
pages = {113-133},
title = {A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Dirichlet's condition},
url = {http://eudml.org/doc/280775},
volume = {93},
year = {2008},
}

TY - JOUR
AU - Lucjan Sapa
TI - A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Dirichlet's condition
JO - Annales Polonici Mathematici
PY - 2008
VL - 93
IS - 2
SP - 113
EP - 133
AB - We deal with a finite difference method for a wide class of nonlinear, in particular strongly nonlinear or quasi-linear, second-order partial differential functional equations of parabolic type with Dirichlet's condition. The functional dependence is of the Volterra type and the right-hand sides of the equations satisfy nonlinear estimates of the generalized Perron type with respect to the functional variable. Under the assumptions adopted, quasi-linear equations are a special case of nonlinear equations. Quasi-linear equations are also treated separately. It is proved that our numerical methods are consistent, convergent and stable. Error estimates are given. The proofs are based on the comparison technique. Examples of physical applications and numerical experiments are presented.
LA - eng
KW - nonlinear and quasi-linear differential functional equations of parabolic type; finite difference methods; stability; convergence; nonlinear estimates of the generalized Perron type; consistency; error estimates; numerical experiments
UR - http://eudml.org/doc/280775
ER -