Title: On a variable step size modification of Hines' method in computational neuroscience,
Abstract: For simulating large networks of neurons Hines proposed a method which uses
extensively the structure of the arising systems of ordinary differential
equations in order to obtain an efficient implementation. The original method
requires constant step sizes and produces the solution on a staggered grid. In
the present paper a one-step modification of this method is introduced and
analyzed with respect to their stability properties. The new method allows for
step size control. Local error estimators are constructed. The method has been
implemented in matlab and tested using simple Hodgkin-Huxley type models.
Comparisons with standard state-of-the-art solvers are provided.