Parameter-uniform convergence analysis of a domain decomposition method for singularly perturbed parabolic problems with Robin boundary conditions

Abstract We construct and analyze a domain decomposition method to solve class of singularly perturbed parabolic problems reaction-diffusion type having Robin boundary conditions. The considers three subdomains, which two are finely meshed, the other is coarsely meshed. partial differential equation associated with problem discretized using finite difference scheme on each subdomain, while conditions approximated special maintain accuracy. Then, an iterative algorithm introduced, where transmission information neighbours done piecewise linear interpolation. It proved that resulting numerical approximations parameter-uniform and, more interestingly, convergence iterates optimal for small values perturbation parameters. results support theoretical about convergence.