Communications of the
Korean Mathematical Society CKMS

This article devises an exponentially fitted method for the numerical solution of two parameter singularly perturbed parabolic boundary value problems. The proposed scheme is able to resolve the two lateral boundary layers of the solution. Error estimates show that the constructed scheme is parameter-uniformly convergent with a quadratic numerical rate of convergence. Some numerical test examples are taken from recently published articles to confirm the theoretical results and demonstrate a good performance of the current scheme.

Keywords: Singularly perturbed, exponentially fitted, finite difference method, two-parameter, parameter uniform

MSC numbers: 65M06, 65M12, 65M15, 65M50