Mesh approximation of singularly perturbed boundary-value problems for systems of elliptic and parabolic equations

TLDR: In this paper, the first boundary value problem is considered in a strip for a system of two parabolic equations in which the parameter multiplying the highest derivatives takes arbitrary values from the half-interval (0, 1).

Abstract: The first boundary-value problem is considered in a strip for a system oftwo parabolic equations in which the parameter multiplying the highest derivatives takes arbitrary values from the half-interval (0, 1]. When the parameter is zero, the system of parabolic equations degenerates into a system of hyperbolic equations which contains no derivatives with respect to the space variables. Difference schemes for the problem, which converge uniformly with respect to the parameter, are constructed using the clustering mesh method. Schemes for the Dirichlet problem in the case ofa system of singularly perturbed elliptic equations which degenerate into equations of zero order are also considered.