The boundary value problem for a singularly perturbed parabolic PDE with convection is considered on an interval in the case of the singularly perturbed Robin boundary condition; the highest space derivatives in the equation and in the boundary condition are multiplied by the perturbation parameter $eps$.In contrast to a Dirichlet boundary value problem, for the problem under consideration the errors of well known classical methods, generally speaking, grow without bound as $eps ll N^{-1}$ where $N$ defines the number of mesh points with respect to $x$.The order of convergence for known $eps$-uniformly convergent schemes does not exceed $1$., In this paper, using a defect correction technique we construct$eps$-uniformly convergent schemes of high-order time-accuracy.The efficiency of the new defect-correction schemes is confirmed with numerical experiments. An original technique for experimental studying of convergence orders is developed for cases when the orders of convergence in the$x$-direction and in the $t$-direction can be essentially different.

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

Hemker, P.W, Shishkin, G.I, & Shishkina, L.P. (2002). High-order time-accurate schemes for singularly perturbed parabolic convection-diffusion problems with Robin boundary conditions. Modelling, Analysis and Simulation [MAS]. CWI.