Efficiency.

In AUTO, efficiency has at times been sacrificed for generality of programming. This applies in particular to computations in which AUTO generates an extended system, for example, computations with ISW=2. However, the user has significant control over computational efficiency, in particular through judicious choice of the AUTO-constants DS, DSMIN, and DSMAX, and, for ODEs, NTST and NCOL. Initial experimentation normally suggests appropriate values.

Slowly varying solutions to ODEs can often be computed with remarkably small values of NTST and NCOL, for example, NTST=5, NCOL=2. Generally, however, it is recommended to set NCOL=4, and then to use the ``smallest'' value of NTST that maintains convergence.

The choice of the pseudo-arclength stepsize parameters DS, DSMIN, and DSMAX is highly problem dependent. Generally, DSMIN should not be taken too small, in order to prevent excessive step refinement in case of non-convergence. It should also not be too large, in order to avoid instant non-convergence. DSMAX should be sufficiently large, in order to reduce computation time and amount of output data. On the other hand, it should be sufficiently small, in order to prevent stepping over bifurcations without detecting them. For a given equation, appropriate values of these constants can normally be found after some initial experimentation.

The constants ITNW, NWTN, THL, EPSU, EPSL, EPSS also affect efficiency. Understanding their significance is therefore useful; see Section 10.4 and Section 10.5. Finally, it is recommended that initial computations be done with ILP=0; no fold detection; and ISP=1; no bifurcation detection for ODEs.