pce_ode_hermite, an Octave code which defines and solves a time-dependent scalar exponential decay ODE with uncertain decay coefficient, using a polynomial chaos expansion (PCE), 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 computer code and data files described and made available on this web page are 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.
black_scholes, an Octave code which implements some simple approaches to the Black-Scholes option valuation theory, by Desmond Higham.
hermite_polynomial, an Octave code which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
sde, an Octave code which illustrates the properties of stochastic differential equations, and common algorithms for their analysis, by Desmond Higham;
stochastic_diffusion, MATLAB codes which implement several versions of a stochastic diffusivity coefficient.
stochastic_rk, an Octave code which applies a Runge Kutta (RK) scheme to a stochastic differential equation.