pce_ode_hermite_test

pce_ode_hermite_test, a MATLAB program which calls pce_ode_hermite() to define and solve a time-dependent scalar exponential decay ODE with uncertain decay coefficient, using a polynomial chaos expansion, in terms of Hermite polynomials.

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:

pce_ode_hermite, a MATLAB program which sets up a simple scalar stochastic ordinary differential equation (SODE) for exponential decay with an uncertain decay rate, using a polynomial chaos expansion in terms of Hermite polynomials.

Source Code:

• pce_ode_hermite_test.m, calls all the tests.
• pce_ode_hermite_test.sh, runs all the tests.
• pce_ode_hermite.txt, the output file.

• pce_ode_hermite_test01.m, tests pce_ode_hermite by plotting the computed and exact expected values over the interval [0,2].
• pce_ode_hermite_test02.m, tests pce_ode_hermite by computing the solution up to TF = 2.0 with a sequence of increasing PCE degrees, and then plotting the errors between the computed and exact expected value there.
• expected_value_plot.png, a PNG plot comparing the computed expected value (the first PCE coefficient at each time) versus the known expected value.
• convergence_plot.png, a PNG plot comparing, at time T=2, the known expected value versus the expected values computed by a sequence of PCE's of increasing degree.