Naol Negero - Department of Mathematics, Wollega University, Nekemte, Ethiopia.
Gemechis File Duressa - Department of Mathematics, Jimma University, Jimma, Ethiopia.

This paper deals with a parameter uniform numerical method for singularly perturbed time delayed parabolic convection-diffusion problems. The method consists of a backward-Euler to discretize in temporal dimension and exponentially fitted B-spline collocation scheme for the spatial dimension on a uniform mesh. Parameter-uniform error estimates are obtained, and the method is proved uniformly convergent. The developed scheme is tested on various problems and observed to support the theoretical results. Finally, the numerical solutions are compared with the existing literature methods, and the present method is more accurate.

Singularly perturbed parabolic convection-diffusion problem, time delay, B-spline collocation, exponentially fitted method, parameter uniform convergence