Discretization.

AUTO discretizes ODE boundary value problems (which includes periodic solutions) by the method of orthogonal collocation using piecewise polynomials with 2-7 collocation points per mesh interval (dBSw:73 dBSw:73). The mesh automatically adapts to the solution to equidistribute the local discretization error (RuCr:78 RuCr:78). The number of mesh intervals and the number of collocation points remain constant during any given run, although they may be changed at restart points. The implementation is AUTO-specific. In particular, the choice of local polynomial basis and the algorithm for solving the linearized collocation systems were specifically designed for use in numerical bifurcation analysis.