alpert_rule


alpert_rule, a Python code which has tabulated values that define Alpert quadrature rules of a number of orders of accuracy for functions that are regular, log singular, or power singular.

The rules defined here assume that the integral is to be taken over the interval [0,1]. The interval is divided into N+1 intervals. The leftmost and rightmost intervals are handled in a special way, depending on whether a particular kind of singularity is expected.

A singularity may exist at the left endpoint, x = 0. The cases are:

In case one, the regular Alpert rule is used in both end intervals. In case two, the power singular Alpert rule is used in the leftmost interval. In case three, the log singular Alpert rule is used in the leftmost interval.

Licensing:

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

Languages:

alpert_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

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Reference:

  1. Bradley Alpert,
    Hybrid Gauss-Trapezoidal Quadrature Rules,
    SIAM Journal on Scientific Computing,
    Volume 20, Number 5, pages 1551-1584, 1999.

Source Code:


Last revised on 17 January 2020.