High-Order Time-Accurate Parallel Schemes for Parabolic Singularly Perturbed Problems with Convection

The first boundary value problem for a singularly perturbed parabolic equation of convection-diffusion type on an interval is studied. For the approximation of the boundary value problem we use earlier developed finite difference schemes, e-uniformly of a high order of accuracy with respect to time, based on defect correction. New in this paper is the introduction of a partitioning of the domain for these e-uniform schemes. We determine the conditions under which the difference schemes, applied independently on subdomains may accelerate (e-uniformly) the solution of the boundary value problem without losing the accuracy of the original schemes. Hence, the simultaneous solution on subdomains can in principle be used for parallelization of the computational method