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<html>
<head>
<title>
DIFFER - Finite Difference Approximations to Derivatives
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
DIFFER <br> Finite Difference Approximations to Derivatives
</h1>
<hr>
<p>
<b>DIFFER</b>
is a C++ library which
determines the finite difference coefficients necessary in order to
combine function values at known locations to compute an approximation
of given accuracy to a derivative of a given order.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files 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>DIFFER</b> is available in
<a href = "../../c_src/differ/differ.html">a C version</a> and
<a href = "../../cpp_src/differ/differ.html">a C++ version</a> and
<a href = "../../f77_src/differ/differ.html">a FORTRAN77 version</a> and
<a href = "../../f_src/differ/differ.html">a FORTRAN90 version</a> and
<a href = "../../m_src/differ/differ.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/divdif/divdif.html">
DIVDIF</a>,
a C++ library which
uses divided differences to compute the polynomial interpolant
to a given set of data.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Ake Bjorck, Victor Pereyra,<br>
Solution of Vandermonde Systems of Equations,<br>
Mathematics of Computation,<br>
Volume 24, Number 112, October 1970, pages 893-903.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "differ.cpp">differ.cpp</a>, the source code.
</li>
<li>
<a href = "differ.hpp">differ.hpp</a>, the include file.
</li>
<li>
<a href = "differ.sh">differ.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "differ_prb.cpp">differ_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "differ_prb.sh">differ_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "differ_prb_output.txt">differ_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>DIFFER_BACKWARD</b> computes backward difference coefficients.
</li>
<li>
<b>DIFFER_CENTRAL</b> computes central difference coefficients.
</li>
<li>
<b>DIFFER_FORWARD</b> computes forward difference coefficients.
</li>
<li>
<b>DIFFER_INVERSE</b> returns the inverse of the DIFFER matrix.
</li>
<li>
<b>DIFFER_MATRIX</b> computes the stencil matrix from the stencil vector.
</li>
<li>
<b>DIFFER_SOLVE</b> solves for finite difference coefficients.
</li>
<li>
<b>DIFFER_STENCIL</b> computes finite difference coefficients.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>I4_TO_STRING</b> converts an I4 to a C++ string.
</li>
<li>
<b>INVERSE_ERROR</b> determines the error in an inverse matrix.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8_FACTORIAL</b> computes the factorial of N.
</li>
<li>
<b>R8MAT_FS_NEW</b> factors and solves a system with one right hand side.
</li>
<li>
<b>R8MAT_MM_NEW</b> multiplies two matrices.
</li>
<li>
<b>R8MAT_MV_NEW</b> multiplies a matrix times a vector.
</li>
<li>
<b>R8MAT_NORM_FRO</b> returns the Frobenius norm of an R8MAT.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8MAT_SUB_NEW</b> computes C = A - B.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01_NEW</b> returns a new unit pseudorandom R8VEC.
</li>
<li>
<b>R8VEC2_PRINT</b> prints an R8VEC2.
</li>
<li>
<b>R8VM_SL</b> solves a R8VM system.
</li>
<li>
<b>R8VM_SL_NEW</b> solves a R8VM system.
</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 = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 03 November 2013.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>