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21st GAMM-Seminar Leipzig on
Robust Fast Solvers

Max-Planck-Institute for Mathematics in the Sciences
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  21st GAMM-Seminar
January, 26th-28th, 2005
 
     
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  Abstract Ivan Gavriljuk, Fri, 13.50-14.10 Previous Contents Next  
  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 time-dependent 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 vector-valued 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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Last updated:
28.01.2005 Impressum
 
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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