A uniformly convergent numerical scheme for two parameters singularly perturbed parabolic convection–diffusion problems with a large temporal lag

Abstract

In the present paper, an exponentially fitted numerical scheme is constructed and analyzed for solving singularly perturbed two-parameter parabolic problems with large temporal lag. The problem is discretized by the Crank–Nicolson scheme and the exponentially fitted cubic spline scheme for temporal and spatial derivatives respectively. The resulting scheme is shown to be second-order convergent both in the temporal and spatial directions. Two numerical examples are presented to support the theoretical analysis developed in this article. The present numerical results are compared with the results in the literature which confirm the efficiency of the present scheme.

Keywords

• Singular perturbation
• Two small parameters
• Parabolic convection–diffusion problem
• Time delay
• Exponentially fitted cubic spline method