Long-time numerical solution of a parabolic equation with memory

Thomée, Vidar; Wahlbin, Lars B.

doi:10.1090/S0025-5718-1994-1220827-1

Long-time numerical solution of a parabolic equation with memory
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by Vidar Thomée and Lars B. Wahlbin PDF

Math. Comp. 62 (1994), 477-496 Request permission

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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