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Approximate solution of a parabolic equation with the use of a rational approximation to the operator exponential

Approximate solution of a parabolic equation with the use of a rational approximation to the... For the abstract parabolic equation $$\dot x = Bx + bv\left( t \right)$$ x ˙ = B x + b v ( t ) with an unbounded self-adjoint operator B, where b is a vector and v(t) is a scalar function, we suggest a solution method based on the evaluation of some rational function of the operator B. We obtain a priori estimates of the approximation error for the output function y(t) = <x(t), l>, where l is a given vector. The results of a numerical experiment for the inhomogeneous heat equation are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Approximate solution of a parabolic equation with the use of a rational approximation to the operator exponential

Differential Equations , Volume 53 (3) – Apr 18, 2017

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References (30)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266117030107
Publisher site
See Article on Publisher Site

Abstract

For the abstract parabolic equation $$\dot x = Bx + bv\left( t \right)$$ x ˙ = B x + b v ( t ) with an unbounded self-adjoint operator B, where b is a vector and v(t) is a scalar function, we suggest a solution method based on the evaluation of some rational function of the operator B. We obtain a priori estimates of the approximation error for the output function y(t) = <x(t), l>, where l is a given vector. The results of a numerical experiment for the inhomogeneous heat equation are presented.

Journal

Differential EquationsSpringer Journals

Published: Apr 18, 2017

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