CONTINUATION
A Sample 2D Continuation Code

CONTINUATION is a MATLAB library which implements the continuation method for a simple 2D problem, which involves finding a point on the unit circle, and then finding a sequence of nearby points which trace out the full curve, using only the information available in the implicit definition of the curve from the function f(x,y)=x^2+y^2-1.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

CONTINUATION is available in a MATLAB version.

Related Data and Programs:

continuation_test

PITCON66, a FORTRAN77 library which seeks to produce a sequence of points that satisfy a set of nonlinear equations with one degree of freedom; this is version 6.6 of ACM TOMS algorithm 596.

PITCON7, a FORTRAN90 library which seeks to produce a sequence of points that satisfy a set of nonlinear equations with one degree of freedom; this is version 7.0 of ACM TOMS algorithm 596.

TEST_CON, a MATLAB library which implements test problems for numerical continuation.

TOMS502, a FORTRAN77 library which seeks to produce a sequence of points that satisfy a set of nonlinear equations with one degree of freedom; this library is commonly called DERPAR;
this is ACM TOMS algorithm 502.

TOMS596, a FORTRAN77 library which seeks to produce a sequence of points that satisfy a set of nonlinear equations with one degree of freedom; this library is commonly called PITCON;
this is ACM TOMS algorithm 596.

Reference:

1. Cor den Heijer, Werner Rheinboldt,
   On Steplength Algorithms for a Class of Continuation Methods,
   SIAM Journal on Numerical Analysis,
   Volume 18, Number 5, October 1981, pages 925-947.
2. Werner Rheinboldt,
   Solution Field of Nonlinear Equations and Continuation Methods,
   SIAM Journal on Numerical Analysis,
   Volume 17, Number 2, April 1980, pages 221-237.
3. Werner Rheinboldt,
   Numerical Analysis of Continuation Methods for Nonlinear Structural Problems,
   Computers and Structures,
   Volume 13, 1981, pages 103-114.
4. Werner Rheinboldt, John Burkardt,
   A Locally Parameterized Continuation Process,
   ACM Transactions on Mathematical Software,
   Volume 9, Number 2, June 1983, pages 215-235.
5. Werner Rheinboldt, John Burkardt,
   Algorithm 596: A Program for a Locally Parameterized Continuation Process,
   ACM Transactions on Mathematical Software,
   Volume 9, Number 2, June 1983, pages 236-241.

Source Code:

• newton.m, uses Newton's method to solve the augmented nonlinear system.
• r8vec_print.m, prints an R8VEC.
• step.m, takes one continuation step.
• tangent.m, computes the tangent vector.
• timestamp.m, prints the current YMDHMS date as a time stamp.