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<html>
<head>
<title>
ODE_SWEEP_SERIAL - Analyze an ODE Solution for Many Parameter Values
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ODE_SWEEP_SERIAL <br> Analyze an ODE Solution for Many Parameter Values
</h1>
<hr>
<p>
<b>ODE_SWEEP_SERIAL</b>
is a directory which
computes the solution of an ODE for many parameter values, keeping track
of the maximum absolute value of the solution.
</p>
<p>
Consider the parameterized second order differential equation:
<pre>
m x'' + b x' + k x = 0
</pre>
which represents the behavior of a spring mass system with a
mass of <b>m</b>, a spring constant of <b>k</b> and a damping
coefficient <b>b</b>.
</p>
<p>
We now suppose that we are interested in properties of the solution <b>x(t)</b>
over the time interval from 0 to 25 seconds, as we vary the physical properties
<b>b</b> and <b>k</b>. In particular, we would like to know the maximum value
of <b>x(t)</b> over the time interval for each choice of the physical parameters.
</p>
<p>
To answer this question, we must solve the ODE for each choice of the parameters.
</p>
<p>
The basic function has the form:
<blockquote>
function peakVals = ode_fun ( bVals, kVals )
</blockquote>
where
<ul>
<li>
bVals is an array of B values;
</li>
<li>
kVals is an array of K values;
</li>
<li>
peakVals is an array containing the maximum value of the ODE solution
for each combination of B and K.
</li>
</ul>
</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>ODE_SWEEP_SERIAL</b> is available in
<a href = "../../m_src/ode_sweep_serial/ode_sweep_serial.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/collatz/collatz.html">
COLLATZ</a>,
a MATLAB library which
computes and analyzes the Collatz
sequence (or "hailstone" sequence or "3n+1 sequence");
</p>
<p>
<a href = "../../m_src/fft_serial/fft_serial.html">
FFT_SERIAL</a>,
a MATLAB program which
demonstrates the computation of a Fast Fourier Transform,
and is intended as a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../m_src/fire_serial/fire_serial.html">
FIRE_SERIAL</a>,
a MATLAB program which
simulates a forest fire over a rectangular array of trees,
starting at a single random location. It is intended as a starting
point for the development of a parallel version.
</p>
<p>
<a href = "../../m_src/md/md.html">
MD</a>,
a MATLAB program which
carries out a molecular dynamics simulation, and is intended as
a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../m_src/mxm/mxm.html">
MXM</a>,
a MATLAB program which
sets up a matrix multiplication problem A=B*C,
intended as a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../m_src/poisson_serial/poisson_serial.html">
POISSON_SERIAL</a>,
a MATLAB program which
computes an approximate solution to the Poisson equation in a rectangle,
and is intended as the starting point for the creation of a parallel version.
</p>
<p>
<a href = "../../m_src/prime_serial/prime_serial.html">
PRIME_SERIAL</a>,
a MATLAB program which
counts the number of primes between 1 and N,
intended as a starting point for the creation of a parallel version.
</p>
<p>
<a href = "../../m_src/quad_serial/quad_serial.html">
QUAD_SERIAL</a>,
a MATLAB program which
approximates an integral using a quadrature rule,
and is intended as a starting point for parallelization exercises.
</p>
<p>
<a href = "../../m_src/quad2d_serial/quad2d_serial.html">
QUAD2D_SERIAL</a>,
a MATLAB program which
approximates an integral over a 2D region using a product quadrature rule,
and is intended as a starting point for parallelization exercises.
</p>
<p>
<a href = "../../m_src/satisfy/satisfy.html">
SATISFY</a>,
a MATLAB program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem.
</p>
<p>
<a href = "../../m_src/search_serial/search_serial.html">
SEARCH_SERIAL</a>,
a MATLAB program which
searches the integers from A to B for a value J such that F(J) = C.
this version of the program is intended as a starting point for
a parallel approach.
</p>
<p>
<a href = "../../m_src/timer/timer.html">
TIMER</a>,
MATLAB programs which
demonstrate how to compute CPU time or elapsed time.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "ode_fun.m">ode_fun.m</a>,
the function which performs the calculations.
</li>
<li>
<a href = "ode_system.m">ode_system.m</a>,
a function which redefines the second order ODE as a pair of first order
ODE's, suitable for treatment by MATLAB's ODE solvers.
</li>
<li>
<a href = "ode_display.m">ode_display.m</a>,
a script which displays a contour plot of the results of the parameter sweep.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "ode_script.m">ode_script.m</a>,
sets up a parameter sweep and runs the code.
</li>
<li>
<a href = "ode_script_output.txt">ode_script_output.txt</a>,
the output file.
</li>
<li>
<a href = "ode_display.png">ode_display.png</a>,
a surface plot of the data XMAX(B,K) computed by the program.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 18 June 2012.
</i>
<!-- John Burkardt -->
</body>
</html>