Available as effic84.pdf.
Describes an algorithm that is responsible for much of NEURON's computational efficiency in dealing with models of cells with complex branched architecture.
Efficient computation of branched nerve equations
Title  Efficient computation of branched nerve equations 
Publication Type  Journal Article 
Year of Publication  1984 
Authors  Hines, M. L. 
Journal  International journal of biomedical computing 
Volume  15 
Pagination  69–76 
Abstract  Three simple improvements are presented which, for a given accuracy, result in a 10–20fold decrease in computation time for simulation of arbitrarily branched active cables with Hodgkin Huxley (HH) kinetics. The first improvement takes advantage of the essentially tridiagonal character of the matrix equation for each branch of a ‘tree’ network and solves the equations as efficiently as for an unbranched cable. The second improvement evaluates the HH membrane conductances at the midpoint of a time step, Δt, to maintain full second order accuracy, 0(Δt^{2}), with no increase in the number of computational steps. The third improvement makes use of ‘premultiplied’ HH rate function tables for very efficient second order correct integration of HH membrane conductance. 
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