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Long-Time Numerical Solution of a Parabolic Equation with Memory

Vidar Thomée and Lars B. Wahlbin
Mathematics of Computation
Vol. 62, No. 206 (Apr., 1994), pp. 477-496
DOI: 10.2307/2153519
Stable URL: http://www.jstor.org/stable/2153519
Page Count: 20
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Long-Time Numerical Solution of a Parabolic Equation with Memory
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Abstract

Long-time stability and convergence properties of two time-discretization methods for an integro-differential equation of parabolic type are studied. The methods are based on the standard backward Euler and second-order backward differencing methods. The memory term is approximated by a quadrature rule, with emphasis on such rules with reduced computational memory requirements. Discretization of the spatial partial differential operators by the finite element method is also considered.

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