Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

On the discretization in time of semilinear parabolic equations with nonsmooth initial data


Authors: Michel Crouzeix and Vidar Thomée
Journal: Math. Comp. 49 (1987), 359-377
MSC: Primary 65M10
MathSciNet review: 906176
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M10

Retrieve articles in all journals with MSC: 65M10


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1987-0906176-3
PII: S 0025-5718(1987)0906176-3
Article copyright: © Copyright 1987 American Mathematical Society