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# Exercise: Speed Comparison

The numerical advantage of implicit methods is that you can use a much larger time step in order to compute the same neuronal model (this is due to the stiffness of the system, see [8]). In order to examine the dependence of the results on the time step you can run a simulation with and without `hsolve` while varying the time step. However In this exercise we are concerned about something completely different: hsolve optimizes the calculations such that it runs faster than the original compartments. The speed advantage by using `hsolve` is given in table 2.1.

Table: Simulating a Purkinje cell containing 4000 compartments without and with `hsolve` in the different chanmodes. The table lists two times three trials: the first set of trials is done without any output. The second set is obtained while plotting the membrane potential of the soma. All numbers give the total CPU time needed to simulate 1000 steps, all simulations used the same time step.
no Xodus output
original | 66.30 | 66.44 | 66.41
chanmode 0 | 56.79 | 56.76 | 56.81
chanmode 1 | 40.26 | 40.27 | 40.34
chanmode 2 | 15.45 | 15.27 | 15.31
chanmode 3 | 14.02 | 13.90 | 13.90
chanmode 4 | 16.47 | 15.96 | 16.05
chanmode 5 | 16.99 | 16.55 | 16.49
Xodus output
original | 66.55 | 66.60 | 66.63
chanmode 0 | 57.14 | 57.05 | 57.05
chanmode 1 | 40.60 | 40.67 | 40.64
chanmode 2 | 15.29 | 15.51 | 15.41
chanmode 3 | 14.08 | 14.08 | 14.20
chanmode 4 | 16.34 | 16.32 | 16.36
chanmode 5 | 16.63 | 16.85 | 16.81

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