Faster simulations of action potential propagation using the newton method
A system of differential equations establishing a two-parallel-fiber geometry with Hodgkin-Huxley membrane properties was integrated with the trapezoidal rule, an implicit integration scheme. The resulting nonlinear system of equations was restated in a form that could be solved by the Newton method, a method new to electrophysiology simulations. The accuracy and stability with regard to the timestep, Δt, of this newer method was compared to that of two other numerical integration schemes, an explicit method and a semi-implicit (Crank-Nicolson') method. For this problem, the trapezoidal rule-Newton method had tremendous advantages over the other two methods in stability and accuracy. For solutions of equivalent accuracy the trapezoidal rule-Newton method required about 2 % of the CPU time required by the explicit method and 35% of the time required by the semi-implicit method.
