continuation
continuation,
a MATLAB code 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^21.
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
test_con,
a MATLAB code which
implements test problems for numerical continuation.
Reference:

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 925947.

Werner Rheinboldt,
Solution Field of Nonlinear Equations and Continuation Methods,
SIAM Journal on Numerical Analysis,
Volume 17, Number 2, April 1980, pages 221237.

Werner Rheinboldt,
Numerical Analysis of Continuation Methods for Nonlinear
Structural Problems,
Computers and Structures,
Volume 13, 1981, pages 103114.

Werner Rheinboldt, John Burkardt,
A Locally Parameterized Continuation Process,
ACM Transactions on Mathematical Software,
Volume 9, Number 2, June 1983, pages 215235.

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 236241.
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.
Last modified on 15 September 2019.