disk01_integrands

disk01_integrands, a MATLAB code which defines several integrands over the unit disk, to check the accuracy of quadrature rules.

Currently, the test integrals include:

1. x^e, where the parameter e is set by the user.
2. r^e, where the parameter e is set by the user.
3. exp(x)

Licensing:

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

Languages:

disk01_integrands is available in a MATLAB version and a Python version.

Related Data and Programs:

disk01_integrands_test

disk_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of a disk of radius R centered at the origin.

quadrule, a MATLAB code which defines quadrature rules on a variety of intervals with different weight functions.

stroud, a MATLAB code which defines quadrature rules for a variety of M-dimensional regions, including the interior of the square, cube and hypercube, the pyramid, cone and ellipse, the hexagon, the M-dimensional octahedron, the circle, sphere and hypersphere, the triangle, tetrahedron and simplex, and the surface of the circle, sphere and hypersphere.

sphere_integrals, a MATLAB code which can be used to test algorithms for quadrature over the surface of the unit sphere in 3D.

triangle_integrals, a MATLAB code which implements test functions for integration over the interior of a triangle in 2D.

Source Code:

• disk_unit_area.m returns the area of the unit disk.
• disk_unit_sample.m returns sample points from the unit disk.
• cos_power_int.m evaluates the cosine power integral.
• p01_exact.m returns the exact integral of test function 1.
• p01_f.m evaluates test function 1.
• p01_parameters.m sets or gets the parameter for test function 1.
• p02_exact.m returns the exact integral of test function 2.
• p02_f.m evaluates test function 2.
• p02_parameters.m sets or gets the parameter for test function 2.
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• p03_exact.m returns the exact integral of test function 3.
• p03_f.m evaluates test function 3.
• sin_power_int.m returns values of the sine power integral.