Approximate solution to abstract differential equations with variable domain

Details Approximate solution to abstract differential equations with variable domain Approximate solution to abstract differential equations with variable domain

2010-03-12

arxiv.org/abs/1003.2537v1

Mathematics

Numerical Analysis

Scientific paper

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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