Thome, V and VasudevaMurty, AS (1995) Approximate solution of u'=-A2u using a relation between exp(-tA2) and exp(itA). In: Numerical Functional Analysis And Optimization, 16 (7-8). pp. 1087-1096. (In Press)Full text not available from this repository.
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.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Taylor&Francis.|
|Keywords:||Semigroup;Parabolic Equation;Finite Elements.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Mathematics|
|Date Deposited:||24 Mar 2009 05:06|
|Last Modified:||24 Mar 2009 05:06|
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