Fitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays

Abstract

This paper deals with solution methods for singularly perturbed delay differential equations having delay on the convection and reaction terms. The considered problem exhibits an exponential boundary layer on the left or right side of the domain. The terms with the delay are treated using Taylor?s series approximation and the resulting singularly perturbed boundary value problem is solved using a specially designed exponentially finite difference method. The stability of the scheme is analysed and investigated using a comparison principle and solution bound. The formulated scheme converges uniformly with linear order of convergence. The theoretical findings are validated using three numerical test examples.

Fitted Tension Spline Method for Singularly Perturbed Time Delay Reaction Diffusion Problems

“…Kanth and Kumar in [9][10][11] used the tension spline method to solve singularly perturbed convection-dominated di erential equations. Woldaregay et al [3,[12][13][14][15][16] developed an exponentially tted numerical method for solving di erent singularly perturbed di erential-di erence equations. In [14,17], they proposed the nonstandard nite di erence techniques and the tted mesh methods, respectively.…”