TY  - JOUR
ID  - Kamont2005
LB  - Kamont2005
AU  - Kamont, Zdzisław
TI  - Numerical approximations of difference functional equations and applications
ST  - Numerical approximations of difference functional equations and applications
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2005
VL  - 25
IS  - 1
SP  - 109
EP  - 130
DO  - http://dx.doi.org/10.7494/OpMath.2005.25.1.109
UR  - http://dx.doi.org/10.7494/OpMath.2005.25.1.109
AB  - We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.
KW  - functional differential equations
KW  - stability and convergence
KW  - interpolating operators
KW  - nonlinear estimates of the Perron type
SN  - 1232-9274
ER  -