CONTIN

Systems of n nonlinear equations in (n+1) variables

CONTIN (also known as PITCON) implements a continuation algorithm with an adaptive choice of a local coordinate system. At each computed point one of the variables is chosen as the local coordinate direction for the one-dimensional solution manifold of the problem. From a predicted point along the tangent direction, a chord Newton process is applied to obtain the next point. Facilities are incorporated to determine the presence of target points where a specified variable has a given value, of turning points with respect to any variable, or of simple bifurcation points. The code includes features for explicit computation of target points and turning points.

CONTIN requires a user subroutine for the evaluation of the function and incorporates algorithms for computing finite-difference approximations of the Jacobian, unless a subroutine for the direct computation of the Jacobian is provided. The routines to solve the bordered banded linear systems can be easily exchanged for user-supplied codes. Several different linear solvers are provided with CONTIN.

The software is written in standard ANSI Fortran. Single and double precision versions of the software are available. Machine dependencies are restricted to a single subroutine.

The software can be obtained from netlib (send index from contin).

References:

W. C. Rheinboldt, Numerical Analysis of Parametrized Nonlinear Equations, John Wiley and Sons Inc., New York, 1985.

W. C. Rheinboldt and J. Burkardt, Algorithm 596: A program for a locally parametrized continuation process, ACM Trans. Math. Software 9 (1983), pp. 236--241.

W. C. Rheinboldt and R. Melhem, A comparison of methods for determining turning points of nonlinear equations, Computing 29 (1982), pp. 201--226.

W. C. Rheinboldt and J. Burkardt, A locally parametrized continuation process, ACM Trans. Math. Software 9 (1983), pp. 215--235.

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