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stochastic_rk.html
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<html>
<head>
<title>
STOCHASTIC_RK - Runge-Kutta Integrator for Stochastic Differential Equations
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
STOCHASTIC_RK <br> Runge-Kutta Integrator for Stochastic Differential Equations
</h1>
<hr>
<p>
<b>STOCHASTIC_RK</b>
is a FORTRAN90 library which
implements Runge-Kutta integration methods for stochastic differential equations.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>STOCHASTIC_RK</b> is available in
<a href = "../../c_src/stochastic_rk/stochastic_rk.html">a C version</a> and
<a href = "../../cpp_src/stochastic_rk/stochastic_rk.html">a C++ version</a> and
<a href = "../../f77_src/stochastic_rk/stochastic_rk.html">a FORTRAN77 version</a> and
<a href = "../../f_src/stochastic_rk/stochastic_rk.html">a FORTRAN90 version</a> and
<a href = "../../m_src/stochastic_rk/stochastic_rk.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/black_scholes/black_scholes.html">
BLACK_SCHOLES</a>,
a FORTRAN90 library which
implements some simple approaches to
the Black-Scholes option valuation theory;
</p>
<p>
<a href = "../../f_src/colored_noise/colored_noise.html">
COLORED_NOISE</a>,
a FORTRAN90 library which
generates samples of noise obeying a 1/f^alpha power law.
</p>
<p>
<a href = "../../f_src/feynman_kac_2d/feynman_kac_2d.html">
FEYNMAN_KAC_2D</a>,
a FORTRAN90 program which
demonstrates the use of the Feynman-Kac algorithm for solving
certain partial differential equations.
</p>
<p>
<a href = "../../m_src/pce_legendre/pce_legendre.html">
PCE_LEGENDRE</a>,
a MATLAB program which
assembles the system matrix associated with a polynomal chaos expansion
of a 2D stochastic PDE, using Legendre polynomials;
</p>
<p>
<a href = "../../f_src/pce_ode_hermite/pce_ode_hermite.html">
PCE_ODE_HERMITE</a>,
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.
</p>
<p>
<a href = "../../f_src/pink_noise/pink_noise.html">
PINK_NOISE</a>,
a FORTRAN90 library which
computes a "pink noise" signal obeying a 1/f power law.
</p>
<p>
<a href = "../../f_src/sde/sde.html">
SDE</a>,
a FORTRAN90 library which
illustrates the properties of stochastic differential equations, and
common algorithms for their analysis,
by Desmond Higham;
</p>
<p>
<a href = "../../m_src/stochastic_diffusion/stochastic_diffusion.html">
STOCHASTIC_DIFFUSION</a>,
MATLAB functions which
implement several versions of a stochastic diffusivity coefficient.
</p>
<p>
<a href = "../../m_src/stochastic_gradient_nd_noise/stochastic_gradient_nd_noise.html">
STOCHASTIC_GRADIENT_ND_NOISE</a>,
a MATLAB program which
solves an optimal control problem involving a functional over a system
with stochastic noise.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Jeremy Kasdin,<br>
Runge-Kutta algorithm for the numerical integration of
stochastic differential equations,<br>
Journal of Guidance, Control, and Dynamics,<br>
Volume 18, Number 1, January-February 1995, pages 114-120.
</li>
<li>
Jeremy Kasdin,<br>
Discrete Simulation of Colored Noise and Stochastic Processes
and 1/f^a Power Law Noise Generation,<br>
Proceedings of the IEEE,<br>
Volume 83, Number 5, 1995, pages 802-827.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "stochastic_rk.f90">stochastic_rk.f90</a>, the source code.
</li>
<li>
<a href = "stochastic_rk.sh">stochastic_rk.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "stochastic_rk_prb.f90">stochastic_rk_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "stochastic_rk_prb.sh">stochastic_rk_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "stochastic_rk_prb_output.txt">stochastic_rk_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>RK1_TI_STEP</b> takes one step of a stochastic Runge Kutta scheme.
</li>
<li>
<b>RK2_TI_STEP</b> takes one step of a stochastic Runge Kutta scheme.
</li>
<li>
<b>RK3_TI_STEP</b> takes one step of a stochastic Runge Kutta scheme.
</li>
<li>
<b>RK4_TI_STEP</b> takes one step of a stochastic Runge Kutta scheme.
</li>
<li>
<b>RK1_TV_STEP</b> takes one step of a stochastic Runge Kutta scheme.
</li>
<li>
<b>RK2_TV_STEP</b> takes one step of a stochastic Runge Kutta scheme.
</li>
<li>
<b>RK4_TV_STEP</b> takes one step of a stochastic Runge Kutta scheme.
</li>
<li>
<b>R8_NORMAL_01</b> returns a unit pseudonormal R8.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 19 June 2010.
</i>
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