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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A least squares procedure for the wave equation

Author: Alfred Carasso
Journal: Math. Comp. 28 (1974), 757-767
MSC: Primary 65N05
MathSciNet review: 0373310
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Abstract: We develop and analyze a least squares procedure for approximating the homogeneous Dirichlet problem for the wave equation in a bounded domain $ \Omega $ in $ {R^N}$. This procedure is based on the pure implicit scheme for time differencing. Surprisingly, it is the normal derivative of u rather than u itself which must be included in the boundary functional. This normal derivative is an unknown quantity. We show that it may be set equal to zero while retaining the $ O(k)$ accuracy of the pure implicit scheme. The penalty is that one must use smoother trial functions to obtain this accuracy.

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Article copyright: © Copyright 1974 American Mathematical Society

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