


Abstract
Ivan Gavriljuk, Fri, 13.5014.10

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Duhamel's Like Algorithms for First Order Differential Equations with Operator Coefficient Having an Evolution Domain
Ivan Gavriljuk (Berufsakademie Thüringen)
(joint work with V.Makarov, V.Vasylyk and T.Bohonova)
We propose a new exponentially convergent algorithm for the
solution of the first order differential equation with an operator
coefficient A with the time dependent domain D(t) in a Banach
space X. Starting from the heat equation with timedependent
boundary conditions we introduce a suitable abstract setting of
the initial value problem for first order differential equation in
a Banach space where the domain of the operator coefficient
depends on the parameter t. We introduce a generalization of the
Duhamel's integral for vectorvalued functions in order to
translate this problem into an integral equation
and then approximate it with
exponential accuracy. Our approach uses essentially the operator exponential
and its sparse approximations.




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