pce_ode_hermite


pce_ode_hermite, a MATLAB 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.

Licensing:

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

Languages:

pce_ode_hermite is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

black_scholes, a MATLAB code which implements some simple approaches to the black-scholes option valuation theory, by desmond higham.

hermite_polynomial, a MATLAB code which evaluates the physicist's hermite polynomial, the probabilist's hermite polynomial, the hermite function, and related functions.

pce_ode_hermite_test

sde, a MATLAB code which illustrates the properties of stochastic differential equations, and common algorithms for their analysis, by desmond higham;

stochastic_diffusion, MATLAB functions which implement several versions of a stochastic diffusivity coefficient.

stochastic_rk, a MATLAB code which applies a runge kutta (rk) scheme to a stochastic differential equation.

Reference:

  1. Roger Ghanem, Pol Spanos,
    Stochastic Finite Elements: A Spectral Approach,
    Revised Edition,
    Dover, 2003,
    ISBN: 0486428184,
    LC: TA347.F5.G56.
  2. Dongbin Xiu,
    Numerical Methods for Stochastic Computations: A Spectral Method Approach,
    Princeton, 2010,
    ISBN13: 978-0-691-14212-8,
    LC: QA274.23.X58.

Source Code:


Last modified on 12 January 2021.