A Robust computational method for singularly perturbed delay parabolic convection-diffusion equations arising in the modeling of neuronal variability

Abstract

In this study, a robust computational method involving exponential cubic spline for solving singularly perturbed parabolic convection-diffusion equations arising in the modeling of neuronal variability has been presented. Some numerical examples are considered to validate the theoretical findings. The proposed scheme is shown to be an e-uniformly convergent accuracy of order O(Δt+h^2 ).