A maximum principle for an explicit finite difference scheme approximating the Hodgkin-Huxley model (Q2490357)

This article deals with an analysis of the numerical solution for the general Hodgkin-Huxley model. The \(L^\infty\)-boundedness of the discretized solution and \(L^2\)-convergence of the numerical solution to a unique weak solution are proved. A finite difference method is used to solve the system of one parabolic equation and three ordinary differential equations. A maximum principle for the discrete solutions is proved in order to show the boundedness of the numerical solution. Numerical experiments verifying the theoretical results are presented.