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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the discretization in time of semilinear parabolic equations with nonsmooth initial data
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by Michel Crouzeix and Vidar Thomée PDF
Math. Comp. 49 (1987), 359-377 Request permission

Abstract:

Single-step discretization methods are considered for equations of the form ${u_t} + Au = f(t,u)$, where A is a linear positive definite operator in a Hilbert space H. It is shown that if the method is consistent with the differential equation then the convergence is essentially of first order in the stepsize, even if the initial data v are only in H, but also that, in contrast to the situation in the linear homogeneous case, higher-order convergence is not possible in general without further assumptions on v.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 49 (1987), 359-377
  • MSC: Primary 65M10
  • DOI: https://doi.org/10.1090/S0025-5718-1987-0906176-3
  • MathSciNet review: 906176