A high order robust numerical scheme for the generalized Stein's model of neuronal variability

Abstract

This paper continues the authors's study of robust numerical scheme for generalized Stein's model of neuronal variability, which is a singularly perturbed parabolic partial differential–difference equation with general values of shift arguments. The work on this class of problems is initiated in the papers [K. Bansal and K.K. Sharma, Parameter-robust numerical scheme for time dependent singularly perturbed reaction- diffusion problem with large delay, Numer. Funct. Anal. Optim. 39(2) (2018), pp. 127–154] for unit shift argument and in [K. Bansal and K.K. Sharma, Parameter uniform numerical scheme for time dependent singularly perturbed convection- diffusion-reaction problems with general shift arguments, Numer. Algorithms 75(1) (2017), pp. 113–145] for general shift arguments. In the present paper, this work is further extended to the development of numerical scheme based on Mickens techniques, interpolation and θ scheme. The advantage of this work over the previous research is that it deals with the problem having general values of the shift arguments with higher order of convergence and without any constraints on the number of intervals.