PCE_ODE_HERMITE is a MATLAB library which defines and solves a time-dependent scalar exponential decay ODE with uncertain decay coefficient, using a polynomial chaos expansion, in terms of Hermite polynomials.
The deterministic equation is
du/dt = - alpha * u, u(0) = u0In the stochastic version, it is assumed that the decay coefficient ALPHA is a Gaussian random variable with mean value ALPHA_MU and variance ALPHA_SIGMA^2.
The exact expected value of the stochastic equation is known to be
u(t) = u0 * exp ( t^2/2)This should be matched by the first component of the polynomial chaos expansion.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
PCE_ODE_HERMITE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.
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You can go up one level to the MATLAB source codes.