An 𝜀-uniform method for a class of singularly perturbed parabolic problems with Robin boundary conditions having boundary turning point

Abstract

A class of singularly perturbed parabolic differential equations with Robin type boundary condition having boundary turning point is propounded on a rectangular domain in the [Formula: see text]-[Formula: see text] plane. A numerical method comprising a standard upwind finite difference scheme is formulated on a rectangular piecewise uniform fitted mesh [Formula: see text] and it is proved to be [Formula: see text]-uniform. Furthermore, it is shown that the errors are bounded in the supremum norm by [Formula: see text], where [Formula: see text] is a constant independent of [Formula: see text], [Formula: see text] and the perturbation parameter [Formula: see text]. Numerical results are given to illustrate the analytical results.