THE DOMAIN DECOMPOSITION METHOD IN THE CASE OF NONOVERLAPPING SUBDOMAINS FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATION

摘要

For rather wide classes of singularly perturbed boundary value problems the e-uniformly convergent methods, whose solution errors are independent of the disturbing parameter e, are proposed (e.g., [l]-[6] and references therein). For regular boundary value problems the efficient numerical methods based on the domain decomposition are well known (see, e.g., [7], [8] and references therein). These methods enable one to reduce the solution of rather complex problems to that of problems on simpler domains and, in particular, to parallelize the computations. Among these techniques, the decomposition methods on nonoverlapping subdomains are especially attractive. They allow one to solve intermediate problems using uniform grids on subdomains.