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.

本文继续作者对广义 Stein 神经元变异性模型的稳健数值方案的研究，该模型是具有一般移位参数值的奇异扰动抛物线偏微分差分方程。关于这类问题的工作是在论文 [K. Bansal 和 KK Sharma，具有大延迟的时间相关奇异扰动反应扩散问题的参数稳健数值方案，Numer。功能。肛门。优化。39(2) (2018), pp. 127–154] 用于单位移位参数和 [K. Bansal 和 KK Sharma，具有一般位移参数的时间相关奇异扰动对流-扩散-反应问题的参数统一数值方案，数。算法 75(1) (2017), pp. 113–145] 用于一般移位参数。在本文中，这项工作进一步扩展到基于 Mickens 技术、插值和θ方案的数值方案的开发。与之前的研究相比，这项工作的优势在于它处理具有更高收敛阶数的移位参数的一般值的问题，并且对间隔数量没有任何限制。