Approximation of systems of convection-diffusion elliptic equations with parabolic boundary layers (Q1608273)

The author considers the Dirichlet problem for a system of two singularly perturbed elliptic equations with convective terms. The perturbation parameter \({\varepsilon}_i\) \((i=1,2)\) multiplying the highest derivative in the \(i\)th equation can take arbitrary values within the half-open interval \((0,1]\). The method of condensing grids and classical difference approximations of the boundary value problem are employed to construct special difference schemes that are uniformly convergent in \({\varepsilon}_1\) and \({\varepsilon}_2\).