chebyshev1_rule

chebyshev1_rule, a Python code which generates a specific Gauss-Chebyshev type 1 quadrature rule, based on user input.

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

The Gauss Chevbyshev type 1 quadrature rule is used as follows:

        Integral ( A <= x <= B ) f(x) / sqrt ( ( x - A ) * ( B - x ) ) dx
      

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

Usage:

chebyshev1_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 files: filename_w.txt, filename_x.txt, and filename_r.txt, containing the weights, abscissas, and interval limits.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

chebyshev1_rule is available in a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

python_rule, a Python code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).

Source Code:

• chebyshev1_rule.py, the source code.
• chebyshev1_rule.sh, runs all the tests.
• chebyshev1_rule.txt, the output file.

• cheby1_o5_r.txt, the region file.
• cheby1_o5_w.txt, the weight file.
• cheby1_o5_x.txt, the abscissa file.