Modelling, Analysis and Simulation High-order time-accurate schemes for singularly perturbed parabolic convection-diffusion problems with Robin boundary conditions

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 ε. 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 ε N−1 where N defines the number of mesh points with respect to x. The order of convergence for known ε-uniformly convergent schemes does not exceed 1. In this paper, using a defect correction technique we construct ε-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. 2000 Mathematics Subject Classification: 65M06; 65M12; 65M15