clenshaw_curtis_rule

clenshaw_curtis_rule, a Python code which generates a Clenshaw Curtis quadrature rule.

The rule is written to three files for easy use as input to other programs.

The standard Clenshaw Curtis quadrature rule is used as follows:

        Integral ( A <= x <= B ) f(x) dx
      

        Sum ( 1 <= i <= order ) w(i) * f(x(i))
      

Usage:

clenshaw_curtis_rule ( order, a, b, 'filename' )

• order is the number of points in the quadrature rule;
• a is the left endpoint;
• b is the right endpoint;
• filename specifies the output filenames: namefile_w.txt, filename_x.txt, and filename_r.txt, containing the weights, abscissas, and interval limits.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

clenshaw_curtis_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

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Reference:

1. Milton Abramowitz, Irene Stegun,
   Handbook of Mathematical Functions,
   National Bureau of Standards, 1964,
   ISBN: 0-486-61272-4,
   LC: QA47.A34.
2. Philip Davis, Philip Rabinowitz,
   Methods of Numerical Integration,
   Second Edition,
   Dover, 2007,
   ISBN: 0486453391,
   LC: QA299.3.D28.
3. Arthur Stroud, Don Secrest,
   Gaussian Quadrature Formulas,
   Prentice Hall, 1966,
   LC: QA299.4G3S7.

Source Code:

• clenshaw_curtis_rule.py the source code.
• clenshaw_curtis_rule.sh runs all the tests.
• clenshaw_curtis_rule.txt the output file.

• cc_o5_r.txt, the region file.
• cc_o5_w.txt, the weight file.
• cc_o5_x.txt, the abscissa file.