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<html>
<head>
<title>
FD1D_BURGERS_LEAP - Finite Difference Non-viscous Burgers Equation, Leapfrog Method
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FD1D_BURGERS_LEAP <br> Finite Difference Non-viscous Burgers Equation, Leapfrog Method
</h1>
<hr>
<p>
<b>FD1D_BURGERS_LEAP</b> is a FORTRAN90 program which
solves the nonviscous time-dependent Burgers equation using finite differences
and the leapfrog method.
</p>
<p>
The function u(x,t) is to be solved for in the equation:
<blockquote>
du/dt + u * du/dx = 0
</blockquote>
for a <= x <= b and t_init <= t <= t_last.
</p>
<p>
Problem data includes an initial condition for u(x,t_init), and the boundary
value functions u(a,t) and u(b,t).
</p>
<p>
The non-viscous Burgers equation can develop shock waves or discontinuities.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>fd1d_burgers_leap</b>
</blockquote>
runs the program.
</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>FD1D_BURGERS_LEAP</b> is available in
<a href = "../../c_src/fd1d_burgers_leap/fd1d_burgers_leap.html">a C version</a> and
<a href = "../../cpp_src/fd1d_burgers_leap/fd1d_burgers_leap.html">a C++ version</a> and
<a href = "../../f77_src/fd1d_burgers_leap/fd1d_burgers_leap.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fd1d_burgers_leap/fd1d_burgers_leap.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fd1d_burgers_leap/fd1d_burgers_leap.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../datasets/burgers/burgers.html">
BURGERS</a>,
a dataset directory which
contains some solutions to the viscous Burgers equation.
</p>
<p>
<a href = "../../f_src/burgers_solution/burgers_solution.html">
BURGERS_SOLUTION</a>,
a FORTRAN90 library which
evaluates an exact solution of the time-dependent 1D viscous Burgers equation.
</p>
<p>
<a href = "../../f_src/fd1d_burgers_lax/fd1d_burgers_lax.html">
FD1D_BURGERS_LAX</a>,
a FORTRAN90 program which
applies the finite difference method and the Lax-Wendroff method
to solve the non-viscous time-dependent Burgers equation
in one spatial dimension.
</p>
<p>
<a href = "../../f_src/fd1d_bvp/fd1d_bvp.html">
FD1D_BVP</a>,
a FORTRAN90 program which
applies the finite difference method
to a two point boundary value problem in one spatial dimension.
</p>
<p>
<a href = "../../f_src/fd1d_heat_explicit/fd1d_heat_explicit.html">
FD1D_HEAT_EXPLICIT</a>,
a FORTRAN90 program which
uses the finite difference method and explicit time stepping
to solve the time dependent heat equation in 1D.
</p>
<p>
<a href = "../../f_src/fd1d_heat_implicit/fd1d_heat_implicit.html">
FD1D_HEAT_IMPLICIT</a>,
a FORTRAN90 program which
uses the finite difference method and implicit time stepping
to solve the time dependent heat equation in 1D.
</p>
<p>
<a href = "../../f_src/fd1d_heat_steady/fd1d_heat_steady.html">
FD1D_HEAT_STEADY</a>,
a FORTRAN90 program which
uses the finite difference method to solve the steady (time independent)
heat equation in 1D.
</p>
<p>
<a href = "../../f_src/fd1d_predator_prey/fd1d_predator_prey.html">
FD1D_PREDATOR_PREY</a>,
a FORTRAN90 program which
implements a finite difference algorithm for predator-prey system
with spatial variation in 1D.
</p>
<p>
<a href = "../../f_src/fd1d_wave/fd1d_wave.html">
FD1D_WAVE</a>,
a FORTRAN90 program which
applies the finite difference method to solve the time-dependent
wave equation utt = c * uxx in one spatial dimension.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Daniel Zwillinger,<br>
Handbook of Differential Equations,<br>
Academic Press, 1997,<br>
ISBN: 0127843965,<br>
LC: QA371.Z88.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fd1d_burgers_leap.f90">fd1d_burgers_leap.f90</a>, the source code.
</li>
<li>
<a href = "fd1d_burgers_leap.sh">fd1d_burgers_leap.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "fd1d_burgers_leap_output.txt">fd1d_burgers_leap_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>FD1D_BURGERS_LEAP</b> solves the nonviscous Burgers equation using leapfrogging.
</li>
<li>
<b>R8VEC_EVEN</b> returns an R8VEC of evenly spaced values.
</li>
<li>
<b>REPORT</b> prints or plots or saves the data at the current time step.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>U_A</b> sets the boundary condition for U at A.
</li>
<li>
<b>U_B</b> sets the boundary condition for U at B.
</li>
<li>
<b>U_INIT</b> sets the initial condition for U.
</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 15 August 2010.
</i>
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