PCE_ODE_HERMITE
Hermite Polynomial Chaos Expansion for a Scalar ODE


PCE_ODE_HERMITE is a C 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) = 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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BLACK_SCHOLES, a C library which implements some simple approaches to the Black-Scholes option valuation theory, by Desmond Higham.

HERMITE_POLYNOMIAL, a C++ library which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.

PCE_BURGERS, a C program which defines and solves a version of the time-dependent viscous Burgers equation, with uncertain viscosity, using a polynomial chaos expansion in terms of Hermite polynomials, by Gianluca Iaccarino.

SDE, a C library which illustrates the properties of stochastic differential equations (SDE's), and common algorithms for their analysis, by Desmond Higham;

STOCHASTIC_RK, a C library 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:

Examples and Tests:

List of Routines:

You can go up one level to the C source codes.


Last modified on 16 September 2012.