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STOCHASTIC_RK\ Runge-Kutta Integrator for Stochastic Differential Equations {#stochastic_rk-runge-kutta-integrator-for-stochastic-differential-equations align=”center”} ============================================================

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

Licensing: {#licensing align=”center”}

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

Languages: {#languages align=”center”}

STOCHASTIC_RK 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: {#related-data-and-programs align=”center”}

BLACK_SCHOLES, a C++ library which implements some simple approaches to the Black-Scholes option valuation theory;

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

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

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

PCE_ODE_HERMITE, a C++ 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 C++ library which computes a “pink noise” signal obeying a 1/f power law.

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

STOCHASTIC_DIFFUSION, a C++ library which implements several versions of a stochastic diffusivity coefficient.

Reference: {#reference align=”center”}

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: {#source-code align=”center”}

• stochastic_rk.cpp, the source code.
• stochastic_rk.hpp, the include file.

Examples and Tests: {#examples-and-tests align=”center”}

• stochastic_rk_prb.cpp, a sample calling program.
• stochastic_rk_prb_output.txt, the output file.

List of Routines: {#list-of-routines align=”center”}

• 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 C++ source codes.

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Last revised on 06 July 2010.