@article{WOLDAREGAY_DURESSA_2019, title={PARAMETER UNIFORM NUMERICAL METHOD FOR SINGULARLY PERTURBED PARABOLIC DIFFERENTIAL DIFFERENCE EQUATIONS}, volume={38}, url={https://ojs.ictp.it/jnms/index.php/jnms/article/view/474}, abstractNote={In this paper, a numerical study is made for solving singularly perturbed differential difference equations with small advance and delay parameters. To approximate the advance and delay terms a Taylor series expansion has been used. The resulting singularly perturbed parabolic PDE is solved by using non-standard finite difference method on uniform mesh in $ x $-direction and implicit Runge-Kutta method is used for the resulting system of IVPs in $ t $-direction. The method is shown to be accurate of order one.  A convergence analysis has been carried out to show $\varepsilon-$ uniform convergence of the proposed scheme. Two numerical examples are considered to investigate parameter uniform convergence of the proposed method.}, number={2}, journal={Journal of the Nigerian Mathematical Society}, author={WOLDAREGAY, M. M. and DURESSA, G. F.}, year={2019}, month={Sep.}, pages={223–245} }