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Approximate solution of u'=-A2u using a relation between exp(-tA2) and exp(itA)

By V Thome and AS VasudevaMurty

Abstract

Let A be a positive definite operator in a Hilbert space and consider the initial value problem for u(t) = -A(2)u. Using a representation of the semigroup exp(-A(2)t) in terms of the group exp(iAt) we express u in terms of the solution of the standard heat equation w(t) = W-yy, with initial values v solving the initial value problem for v(y) = iAv. This representation is used to construct a method for approximating u in terms of approximations of v. In the case that A is a 2(nd) order elliptic operator the method is combined with finite elements in the spatial variable and then reduces the solution of the 4(th) order equation for u to that of the 2(nd) order equation for v, followed by the solution of the heat equation in one space variable

Topics: Mathematics
Publisher: Taylor&Francis
Year: 1995
DOI identifier: 10.1080/01630569508816661
OAI identifier: oai:eprints.iisc.ac.in:19624
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