Gauss-Legendre and Chebyshev quadratures for singular integrals

Exact expressions are presented for efficient computation of the weights in Gauss-Legendre and Chebyshev quadratures for selected singular integrands. The singularities may be of Cauchy type, logarithmic type or algebraic-logarithmic end-point branching points. We provide Fortran 90 routines for computing the weights for both the Gauss-Legendre and the Chebyshev (Fejér-1) meshes whose size can be set by the user.

New program summary

Program title: SINGQUADCatalogue identifier: AEBR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 4128No. of bytes in distributed program, including test data, etc.: 25 815Distribution format: tar.gzProgramming language: Fortran 90Computer: Any with a Fortran 90 compilerOperating system: Linux, Windows, MacRAM: Depending on the complexity of the problemClassification: 4.11Nature of problem: Program provides Gauss-Legendre and Chebyshev (Fejér-1) weights for various singular integrands.Solution method: The weights are obtained from the condition that the quadrature of order N must be exact for a polynomial of degree?(N−1). The weights are expressed as moments of the singular kernels associated with Legendre or Chebyshev polynomials. These moments are obtained in analytic form amenable for computation.Additional comments: If the NAGWare f95 compiler is used, the option, “-kind = byte”, must be included in the compile command lines of the Makefile.Running time: The test run supplied with the distribution takes a couple of seconds to execute.