Approximate solution to abstract differential equations with variable domain
Numerical Analysis
2010-03-15 v1 Functional Analysis
Abstract
A new exponentially convergent algorithm is proposed for an abstract the first order differential equation with unbounded operator coefficient possessing a variable domain. The algorithm is based on a generalization of the Duhamel integral for vector-valued functions. This technique translates the initial problem to a system of integral equations. Then the system is approximated with exponential accuracy. The theoretical results are illustrated by examples associated with the heat transfer boundary value problems.
Cite
@article{arxiv.1003.2537,
title = {Approximate solution to abstract differential equations with variable domain},
author = {T. Ju. Bohonova and I. P. Gavrilyuk and V. L. Makarov and V. Vasylyk},
journal= {arXiv preprint arXiv:1003.2537},
year = {2010}
}