A Practical Algorithm for Solving Dynamic Membrane Equations

TLDR: Many investigators work with the Hodgkin-Huxley model of membrane behavior or extensions thereof, in which action potentials are found as solutions of simultaneous non-linear differential equations which must be solved using numerical techniques on a digital computer.

Abstract: Many investigators work with the Hodgkin-Huxley model of membrane behavior or extensions thereof. In these models action potentials are found as solutions of simultaneous non-linear differential equations which must be solved using numerical techniques on a digital computer. Recent membrane models showing pacemaker activity, such as that of McAllister, Noble, and Tsien, involve solutions covering long periods of time, up to fisve seconds, and many ionic currents. Those added requirements make it desirable to have an efficient algorithm to minimize computer costs, and a systematic and simple solution method to keep the program writing and debugging to manageable levels.