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<html>
<head>
<title>
RK4 - Runge-Kutta 4th Order ODE Solver
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
RK4 <br> Runge-Kutta 4th Order ODE Solver
</h1>
<hr>
<p>
<b>RK4</b>
is a FORTRAN90 library which
implements a simple Runge-Kutta solver for an initial value problem.
</p>
<p>
The <b>rk4()</b> routine does not include any error estimator. It
takes a single step at a time, requiring the user to control the step size.
</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>RK4</b> is available in
<a href = "../../c_src/rk4/rk4.html">a C version</a> and
<a href = "../../cpp_src/rk4/rk4.html">a C++ version</a> and
<a href = "../../f77_src/rk4/rk4.html">a FORTRAN77 version</a> and
<a href = "../../f_src/rk4/rk4.html">a FORTRAN90 version</a> and
<a href = "../../m_src/rk4/rk4.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/nms/nms.html">
NMS</a>,
a FORTRAN90 library which
includes the <b>DDRIV</b> package of ODE solvers.
</p>
<p>
<a href = "../../f_src/ode/ode.html">
ODE</a>,
a FORTRAN90 library which
solves a system of ordinary differential equations,
by Shampine and Gordon.
</p>
<p>
<a href = "../../f77_src/odepack/odepack.html">
ODEPACK</a>,
a FORTRAN77 library which
contains nine ODE solvers, including LSODE, LSODES, LSODA,
LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS,
by Alan Hindmarsh.
</p>
<p>
<a href = "../../f_src/rkf45/rkf45.html">
RKF45</a>,
a FORTRAN90 library which
implements the Runge-Kutta-Fehlberg ODE solver.
</p>
<p>
<a href = "../../f_src/test_ode/test_ode.html">
TEST_ODE</a>,
a FORTRAN90 library which
contains routines which define some test problems for ODE solvers.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Erwin Fehlberg,<br>
Low-order Classical Runge-Kutta Formulas with Stepsize Control,<br>
NASA Technical Report R-315, 1969.
</li>
<li>
Lawrence Shampine, Herman Watts, S Davenport,<br>
Solving Non-stiff Ordinary Differential Equations -
The State of the Art,<br>
SIAM Review,<br>
Volume 18, pages 376-411, 1976.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "rk4.f90">rk4.f90</a>, the source code.
</li>
<li>
<a href = "rk4.sh">rk4.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "rk4_prb.f90">rk4_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "rk4_prb.sh">rk4_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "rk4_prb_output.txt">rk4_prb_output.txt</a>,
the output file.
</li>
<li>
<a href = "rk4_prb.png">rk4_prb.png</a>,
an image of the solution.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>RK4</b> takes one Runge Kutta step.
</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 31 January 2012.
</i>
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