International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 4, Pages 523-536
doi:10.1155/IJMMS.2005.523

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

Abstract

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.