A splitting uniformly convergent method for one-dimensional parabolic singularly perturbed convection-diffusion systems

In this paper we deal with solving robustly and efficiently one-dimensional linear parabolic singularly perturbed systems of convection-diffusion type, where the diffusion parameters can be different at each equation even they have orders magnitude. The numerical algorithm combines classical upwind finite difference scheme to discretize in space fractional implicit Euler method together an appropriate splitting by components time. We prove that if spatial discretization is defined on adequate piecewise uniform Shishkin mesh, fully discrete uniformly convergent first order time almost space. technique used produces only tridiagonal solved level; thus, from computational cost point view, propose more efficient than other algorithms which been for these problems. Numerical results several test problems are shown, corroborate practice both convergence efficiency algorithm.