A differential-equations algorithm for nonlinear equations

DAFNE is a set of FORTRAN subprograms for solving nonlinear equations that implements a method founded on the numerical solution of a Cauchy problem for a system of ordinary differential equahons inspired by classical mechanics. This paper gives a detailed description of the method as implemented in DAFNE and reports on the numerical tests that have been performed; the DAFNE package is described in the accompanying Algorithm. The main conclusions are that DAFNE improves in different substantial respects upon a previous FORTRAN implementation of the same method, and compares favorably with existing software.