Figure 5.

Components of our numerical approach. (A) The Hines algorithm (left) solves the entire neuron implicitly (indicated by blue), represented here as a neuronal arbor comprising branches, compartments, and implicit junctions. Inset image depicts how a parallel solver can calculate this solution, with the matrix A representing the portion of the neuronal arbor that must be solved in a single phase (i.e., the whole tree). (B) Hines’ neuronal splitting algorithm allows different trees originating from the soma to be solved separately and implicitly, here depicted by different colors. The soma is then solved in a manner Hines describe as implicit equivalent (purple). Inset depicts each tree solved in parallel, assigning a different subscript to matrices A_n to represent this parallelism (dotted lines demarcate different trees). (C) Rempe–Chopp's explicit algorithm transforms each branch point into an explicit junction (orange) and all branches can be solved implicitly and in parallel (inset; wherein the matrix A_n indicates parallelism, its subscripts labeled on each branch, and the dotted line demarcates all instances of A_n).