Alternate Overlapping Schwarz Method for Singularly Perturbed Semilinear Convection-Diffusion Problems
We propose an alternate overlapping Schwarz method to solve the singularly perturbed semilinear convection-diffusion problems. The method decomposes the original domain into two overlapping subdomains. One, the outside boundary layer subdomain, and the other, inside boundary layer subdomain. On the outside boundary layer subdomain, a combination of the second order compact difference scheme and central difference scheme with uniform mesh is considered; while on the inside boundary layer subdomain a central difference scheme with a special piecewise-uniform mesh is considered. The convergence analysis is given and the method is shown to have almost second order parameter-uniform convergence. Numerical experiments are presented to demonstrate the efficiency of the method.
KeywordsAlternate overlapping Schwarz method Central difference scheme Compact difference scheme Semilinear convection-diffusion problems Singular perturbation problems
The authors gratefully acknowledge the valuable comments and suggestions from the anonymous referees. The research work of the second author is supported by Council of Scientific and Industrial Research, India.