Comparison of explicit and implicit difference schemes for parabolic functional differential equations

Zdzisław Kamont, and Karolina Kropielnicka. "Comparison of explicit and implicit difference schemes for parabolic functional differential equations." Annales Polonici Mathematici 103.2 (2012): 135-160. <http://eudml.org/doc/280162>.

@article{ZdzisławKamont2012,
abstract = {Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both methods. It is shown that the conditions on the mesh for explicit difference schemes are more restrictive than the suitable assumptions for implicit methods. There are implicit difference schemes which are convergent while the corresponding explicit difference methods are not convergent. Error estimates for both methods are constructed.},
author = {Zdzisław Kamont, Karolina Kropielnicka},
journal = {Annales Polonici Mathematici},
keywords = {functional differential equations; stability and convergence; comparison methods; differential and difference inequalities},
language = {eng},
number = {2},
pages = {135-160},
title = {Comparison of explicit and implicit difference schemes for parabolic functional differential equations},
url = {http://eudml.org/doc/280162},
volume = {103},
year = {2012},
}

TY - JOUR
AU - Zdzisław Kamont
AU - Karolina Kropielnicka
TI - Comparison of explicit and implicit difference schemes for parabolic functional differential equations
JO - Annales Polonici Mathematici
PY - 2012
VL - 103
IS - 2
SP - 135
EP - 160
AB - Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both methods. It is shown that the conditions on the mesh for explicit difference schemes are more restrictive than the suitable assumptions for implicit methods. There are implicit difference schemes which are convergent while the corresponding explicit difference methods are not convergent. Error estimates for both methods are constructed.
LA - eng
KW - functional differential equations; stability and convergence; comparison methods; differential and difference inequalities
UR - http://eudml.org/doc/280162
ER -