We consider the first boundary value problem for a singularly perturbed para-bo-lic PDE with convection on an interval. For the case of sufficiently smooth data, it is easy to construct a standard finite difference operator and a piecewise uniform mesh, condensing in the boundary layer, which gives an $epsilon$-uniformly convergent difference scheme. The order of convergence for such a scheme is exactly one and up to a small logarithmic factor one with respect to the time and space variables, respectively. In this paper we construct high-order time-accurate $epsilon$-uniformly convergent schemes by a defect correction technique. The efficiency of the new defect-correction scheme is confirmed by numerical experiments.

Finite difference methods (msc 65M06), Stability and convergence of numerical methods (msc 65M12), Error bounds (msc 65M15)
Life Sciences (theme 5), Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Scientific Computing

Hemker, P.W, Shishkin, G.I, & Shishkina, L.P. (2001). High-order time-accurate schemes for parabolic singular perturbation problems with convection. Modelling, Analysis and Simulation [MAS]. CWI.