pce_ode_hermite, a Fortran90 code 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) = u0
In 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 information on this web page is distributed under the MIT license.
pce_ode_hermite is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.
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