Robust septic Hermite collocation technique for singularly perturbed generalized Hodgkin–Huxley equation

Abstract

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.

Keywords:

• Hodgkin–Huxley equation
• sixth-order septic Hermite collocation method
• Crank–Nicolson scheme
• Von-Neumann
• quasilinearization

2010 Mathematics Subject Classifications:

• 65Nxx Numerical methods for partia differential equations
• boundary value problems

Acknowledgments

Ms. Archna Kumari is thankful to NPIU, MHRD New Delhi, for providing financial assistance (SRF) under TEQIP-III project.

Disclosure statement

No potential conflict of interest was reported by the author(s).