STOCHASTIC_RK
Runge-Kutta Integrator for Stochastic Differential Equations

STOCHASTIC_RK is a FORTRAN90 library which implements Runge-Kutta integration methods for stochastic differential equations.

Licensing:

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

Languages:

STOCHASTIC_RK 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 FORTRAN90 library which implements some simple approaches to the Black-Scholes option valuation theory;

COLORED_NOISE, a FORTRAN90 library which generates samples of noise obeying a 1/f^alpha power law.

FEYNMAN_KAC_2D, a FORTRAN90 program which demonstrates the use of the Feynman-Kac algorithm for solving certain partial differential equations.

ORNSTEIN_UHLENBECK, a FORTRAN90 library which approximates solutions of the Ornstein-Uhlenbeck stochastic differential equation (SDE) using the Euler method and the Euler-Maruyama method.

PCE_LEGENDRE, a MATLAB program which assembles the system matrix associated with a polynomal chaos expansion of a 2D stochastic PDE, using Legendre polynomials;

PCE_ODE_HERMITE, a FORTRAN90 program which sets up a simple scalar ODE for exponential decay with an uncertain decay rate, using a polynomial chaos expansion in terms of Hermite polynomials.

PINK_NOISE, a FORTRAN90 library which computes a "pink noise" signal obeying a 1/f power law.

SDE, a FORTRAN90 library which illustrates the properties of stochastic differential equations, and common algorithms for their analysis, by Desmond Higham;

STOCHASTIC_DIFFUSION, FORTRAN90 functions which implement several versions of a stochastic diffusivity coefficient.

STOCHASTIC_GRADIENT_ND_NOISE, a MATLAB program which solves an optimal control problem involving a functional over a system with stochastic noise.

Reference:

1. Jeremy Kasdin,
   Runge-Kutta algorithm for the numerical integration of stochastic differential equations,
   Journal of Guidance, Control, and Dynamics,
   Volume 18, Number 1, January-February 1995, pages 114-120.
2. Jeremy Kasdin,
   Discrete Simulation of Colored Noise and Stochastic Processes and 1/f^a Power Law Noise Generation,
   Proceedings of the IEEE,
   Volume 83, Number 5, 1995, pages 802-827.

Source Code:

• stochastic_rk.f90, the source code.

Examples and Tests:

• stochastic_rk_test.f90, a sample calling program.
• stochastic_rk_test.txt, the output file.

List of Routines:

• RK1_TI_STEP takes one step of a stochastic Runge Kutta scheme.
• RK2_TI_STEP takes one step of a stochastic Runge Kutta scheme.
• RK3_TI_STEP takes one step of a stochastic Runge Kutta scheme.
• RK4_TI_STEP takes one step of a stochastic Runge Kutta scheme.
• RK1_TV_STEP takes one step of a stochastic Runge Kutta scheme.
• RK2_TV_STEP takes one step of a stochastic Runge Kutta scheme.
• RK4_TV_STEP takes one step of a stochastic Runge Kutta scheme.
• R8_NORMAL_01 returns a unit pseudonormal R8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.