In this paper, the singularly perturbed generalized Hodgkin–Huxley equation is solved by the septic Hermite collocation method (SHCM). In this method, septic Hermite interpolating polynomials are used to approximate the trial function because of their special properties such as continuity of the function and the continuity of its tangent at the grid points. The Crank–Nicolson scheme is applied for time discretization and the septic Hermite interpolating polynomials are used for space discretization. The Von-Neumann stability analysis is applied and the algorithm is found to be unconditionally stable. The efficiency of the numerical technique is demonstrated by solving some test examples and comparing the output with the literature data. The analysis shows that the present scheme is easy to implement and gives better results in contrast to the earlier ones.

在本文中，奇异摄动的广义 Hodgkin-Huxley 方程通过 septic Hermite 搭配法 (SHCM) 求解。在该方法中，septic Hermite 插值多项式用于逼近试验函数，因为它们具有函数的连续性和网格点处切线的连续性等特殊性质。Crank-Nicolson 方案用于时间离散化，Septic Hermite 插值多项式用于空间离散化。应用冯-诺依曼稳定性分析，发现算法是无条件稳定的。通过解决一些测试示例并将输出与文献数据进行比较，证明了数值技术的效率。