International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 4, Pages 523-536

Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations

Yubin Yan1,2

1Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK
2Department of Automatic Control and Systems Engineering, Faculty of Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK

Received 11 May 2004; Revised 6 December 2004

Copyright © 2005 Yubin Yan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for the approximation of time derivative has been obtained.