Acceleration by Parallel Computations of Solving High-Order Time-Accurate Difference Schemes for Singularly Perturbed Convection-Diffusion Problems

For singularly perturbed convection-diffusion problems with the perturbation parameter εmultiplying the highest derivatives, we construct a scheme based on the defect correction method and its parallel variant that converge ε-uniformly with second-order accuracy in the time variable. We also give the conditions under which the parallel computation accelerates the solution process with preserving the higher-order accuracy of the original schemes.