TY  - JOUR
ID  - Czernous2014
LB  - Czernous2014
AU  - Czernous, Wojciech
AU  - Jaruszewska-Walczak, Danuta
TI  - Difference problems generated by infinite systems of nonlinear parabolic functional differential equations with the Robin conditions
ST  - Difference problems generated by infinite systems of nonlinear parabolic functional differential equations with the Robin conditions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 2
SP  - 311
EP  - 326
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.2.311
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.2.311
AB  - We consider the classical solutions of mixed problems for infinite, countable systems of parabolic functional differential equations. Difference methods of two types are constructed and convergence theorems are proved. In the first type, we approximate the exact solutions by solutions of infinite difference systems. Methods of second type are truncation of the infinite difference system, so that the resulting difference problem is finite and practically solvable. The proof of stability is based on a comparison technique with nonlinear estimates of the Perron type for the given functions. The comparison system is infinite. Parabolic problems with deviated variables and integro-differential problems can be obtained from the general model by specifying the given operators.
KW  - nonlinear parabolic equations
KW  - functional difference equations
KW  - infinite systems
KW  - Volterra type operators
KW  - nonlinear estimates of the Perron type
KW  - truncation methods
SN  - 1232-9274
ER  -