DISK01_QUARTER_RULE
Compute a Quadrature Rule for the Unit Quarter Disk

DISK01_QUARTER_RULE is a MATLAB program which demonstrates how to compute a quadrature rule of a particular precision to estimate integrals over the interior of the unit quarter disk in 2D.

The unit quarter disk in 2D is the set of points (X,Y) such that 0 <= X, 0 <= Y, and X^2+Y^2 <= 1.

The program sets up the nonlinear equations that characterize the points and weights of the rule, and then calls MATLAB's fsolve() function to solve the nonlinear system.

Licensing:

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

Languages:

DISK01_QUARTER_RULE is available in a MATLAB version.

Related Data and Programs:

ANNULUS_RULE, a MATLAB library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

DISK01_QUARTER_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the unit quarter disk in 2D.

disk01_quarter_rule_test

Source Code:

• disk01_quarter_area.m, returns the area of the unit quarter disk.
• disk01_quarter_monomial_integral.m, returns the exact integral of a monomial over the unit quarter disk
• disk01_quarter_rule.m, computes a quadrature rule of precision 2 for the unit quarter disk.
• timestamp.m, prints the YMDHMS date as a timestamp.