Computational method for singularly perturbed parabolic differential equations with discontinuous coefficients and large delay

This paper deals with the computational method for a class of second-order singularly perturbed parabolic differential equations with discontinuous coefficients involving large negative shift. The formulated method comprises the implicit Euler and the cubic-spline in compression methods for time and spatial dimensions, respectively. Intensive numerical experimentation has been done on some model examples and the results are tabulated. The results depict that the present method is more accurate than some methods existing in the literature. Further, the layer behavior of the solutions is presented using graphs and observed to agree with the existing theories. Finally, error analysis of the scheme is done and observed that the proposed method is parameter uniform convergent with the order of convergence (Δt+h2).