Solutions of initial boundary value problems for parabolic functional differential equations are approximated by solutions of implicit difference schemes. The existence and uniqueness of approximate solutions is proved. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. It is shown that the new methods are considerably better than the explicit difference schemes. Numerical examples are presented.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap100-3-3,
author = {Milena Netka},
title = {Implicit difference schemes for mixed problems related to parabolic functional differential equations},
journal = {Annales Polonici Mathematici},
volume = {101},
year = {2011},
pages = {237-259},
zbl = {1213.35398},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap100-3-3}
}
Milena Netka. Implicit difference schemes for mixed problems related to parabolic functional differential equations. Annales Polonici Mathematici, Tome 101 (2011) pp. 237-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap100-3-3/