pitcon66_test

pitcon66_test, a FORTRAN77 code which calls pitcon66(), which carries out the continuation method for producing a series of solutions of a set of nonlinear equations with one degree of freedom.

Licensing:

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

Related Data and Programs:

pitcon66, a FORTRAN77 code which carries out the continuation method for producing a series of solutions of a set of nonlinear equations with one degree of freedom.

Source Code:

• pitcon66_test.sh, runs all the tests.

pitcon66_test1 sets up the Freudenstein Roth function. There are 2 equations, and N = 3 variables. The solution curve has some severe bends.

• pitcon66_test1.f, a sample calling program.
• pitcon66_test1.sh, commands to compile and run the sample program.
• pitcon66_test1.txt, the output file.

pitcon66_test2 sets up the aircraft stability problem, with N = 8. There are 7 equations in N = 8 variables. This is a mildly nonlinear problem, whose solution curve has some limit points that are difficult to track.

• pitcon66_test2.f, a sample calling program.
• pitcon66_test2.sh, commands to compile and run the sample program.
• pitcon66_test2.txt, the output file.

pitcon66_test3 sets up a two point boundary value problem with a parameter, LAMBDA, and variable number set to N = 22. (This problem can easily be modified to use larger values of N). This problem has a limit point in the LAMBDA parameter, which we seek. We solve this problem 6 times, illustrating the use of full and banded jacobians, and of user-generated, or forward or central difference approximated jacobian matrices. The program seeks limit points in LAMBDA.

• pitcon66_test3.f, a sample calling program.
• pitcon66_test3.sh, commands to compile and run the sample program.
• pitcon66_test3.txt, the output file.

pitcon66_test4 sets up the Freudenstein Roth function, with N = 3, and investigates the use of the fixed parameterization option.

• pitcon66_test4.f, a sample calling program.
• pitcon66_test4.sh, commands to compile and run the sample program.
• pitcon66_test4.txt, the output file.

pitcon66_test5 repeats problem 3, the two point boundary value problem. This time, we do NOT seek the limit point in the LAMBDA parameter, but rather the two target points where LAMBDA=0.8, which occurs twice, before and after LAMBDA "goes around the bend". Here, the interest is in investigating the ability to request a full, modified, or "cheap" Newton iteration.

• pitcon66_test5.f, a sample calling program.
• pitcon66_test5.sh, commands to compile and run the sample program.
• pitcon66_test5.txt, the output file.

pitcon66_test6 sets up the Freudenstein Roth function, with N = 3, and investigates the use of the options for checking the accuracty of a user-supplied jacobian. This version of the problem demonstrates the jacobian checking option. Two runs are made. Each is allowed only five steps. The first run is with the correct jacobian. The second run uses a defective jacobian, and demonstrates not only the jacobian checker, but also shows that "slightly" bad jacobians can cause the Newton convergence to become linear rather than quadratic.

• pitcon66_test6.f, a sample calling program.
• pitcon66_test6.sh, commands to compile and run the sample program.
• pitcon66_test6.txt, the output file.

pitcon66_test7 sets up the materially nonlinear rod, with a variety of values of N depending on the user choices for the piecewise polynomial basis and continuity conditions. The program is currently restricted to N=71 variables maximum.

• pitcon66_test7.f, a sample calling program.
• pitcon66_test7.sh, commands to compile and run the sample program.
• pitcon66_test7.txt, the output file.

pitcon66_test8 sets up the Freudenstein Roth function, with N = 3, and investigates the use of the options for approximating the jacobian using finite differences.

• pitcon66_test8.f, a sample calling program.
• pitcon66_test8.sh, commands to compile and run the sample program.
• pitcon66_test8.txt, the output file.