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arXiv · 1003.2537

Approximate solution to abstract differential equations with variable domain

T. Ju. Bohonova·I. P. Gavrilyuk·V. L. Makarov·V. Vasylyk
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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.

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T. Ju. Bohonova, I. P. Gavrilyuk, V. L. Makarov, V. Vasylyk. 2010-03-12. Approximate solution to abstract differential equations with variable domain. https://arxiv.org/abs/1003.2537

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