fd1d_burgers_leap/fd1d_burgers_leap.html

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      FD1D_BURGERS_LEAP - Finite Difference Non-viscous Burgers Equation, Leapfrog Method
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      FD1D_BURGERS_LEAP <br> Finite Difference Non-viscous Burgers Equation, Leapfrog Method
    </h1>

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    <p>
      <b>FD1D_BURGERS_LEAP</b> is a FORTRAN77 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 &lt;= x &lt;= b and t_init &lt;= t &lt;= 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>

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      Usage:
    </h3>

    <p>
      <blockquote>
        <b>fd1d_burgers_leap</b>
      </blockquote>
      runs the program.
    </p>

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      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>

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      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>

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      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 = "../../f77_src/burgers_solution/burgers_solution.html">
      BURGERS_SOLUTION</a>,
      a FORTRAN77 library which
      evaluates an exact solution of the time-dependent 1D viscous Burgers equation.
    </p>

    <p>
      <a href = "../../f77_src/fd1d_burgers_lax/fd1d_burgers_lax.html">
      FD1D_BURGERS_LAX</a>, 
      a FORTRAN77 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 = "../../f77_src/fd1d_bvp/fd1d_bvp.html">
      FD1D_BVP</a>,
      a FORTRAN77 program which
      applies the finite difference method
      to a two point boundary value problem in one spatial dimension.
    </p>

    <p>
      <a href = "../../f77_src/fd1d_heat_explicit/fd1d_heat_explicit.html">
      FD1D_HEAT_EXPLICIT</a>,
      a FORTRAN77 program which
      uses the finite difference method and explicit time stepping 
      to solve the time dependent heat equation in 1D.
    </p>

    <p>
      <a href = "../../f77_src/fd1d_heat_implicit/fd1d_heat_implicit.html">
      FD1D_HEAT_IMPLICIT</a>,
      a FORTRAN77 program which
      uses the finite difference method and implicit time stepping 
      to solve the time dependent heat equation in 1D.
    </p>

    <p>
      <a href = "../../f77_src/fd1d_heat_steady/fd1d_heat_steady.html">
      FD1D_HEAT_STEADY</a>,
      a FORTRAN77 program which
      uses the finite difference method to solve the steady (time independent)
      heat equation in 1D.
    </p>

    <p>
      <a href = "../../f77_src/fd1d_predator_prey/fd1d_predator_prey.html">
      FD1D_PREDATOR_PREY</a>,
      a FORTRAN77 program which
      implements a finite difference algorithm for predator-prey system
      with spatial variation in 1D.
    </p>

    <p>
      <a href = "../../f77_src/fd1d_wave/fd1d_wave.html">
      FD1D_WAVE</a>,
      a FORTRAN77 program which
      applies the finite difference method to solve the time-dependent
      wave equation utt = c * uxx in one spatial dimension.
    </p>

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      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>

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      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "fd1d_burgers_leap.f">fd1d_burgers_leap.f</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>

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      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>

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      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 = "../f77_src.html">
      the FORTRAN77 source codes</a>.
    </p>

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    <i>
      Last revised on 18 August 2010.
    </i>

    <!-- John Burkardt -->

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