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首页> 外文期刊>Computer physics communications >Gauss-Legendre and Chebyshev quadratures for singular integrals
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Gauss-Legendre and Chebyshev quadratures for singular integrals

机译：用于奇异积分的Gauss-Legendre和Chebyshev正交

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摘要

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: SINGQUAD. Catalogue identifier: AEBR_v1_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEBR_v1_0.html. Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html. No. of lines in distributed program, including test data, etc.: 4128. No. of bytes in distributed program, including test data, etc.: 25 815. Distribution format: tar.gz. Programming language: Fortran 90. Computer: Any with a Fortran 90 compiler. Operating system: Linux, Windows, Mac. RAM: Depending on the complexity of the problem. Classification: 4.11. Nature 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.
机译：给出了精确的表达式，可以有效地计算所选奇异积分的Gauss-Legendre和Chebyshev积分中的权重。奇异点可以是柯西类型，对数类型或代数对数端点分支点。我们提供了Fortran 90例程，用于计算Gauss-Legendre和Chebyshev（Fejér-1）网格的权重，这些网格的大小可由用户设置。新程序摘要：程序标题：SINGQUAD。目录标识符：AEBR_v1_0。程序摘要URL：http://cpc.cs.qub.ac.uk/summaries/AEBR_v1_0.html。可从以下网站获得该程序：爱尔兰北卡罗来纳州皇后大学CPC程序库。许可条款：标准CPC许可，http：//cpc.cs.qub.ac.uk/licence/licence.html。分布式程序中的行数，包括测试数据等：4128。分布式程序中的字节数，包括测试数据等：25815。分发格式：tar.gz。编程语言：Fortran90。计算机：带有Fortran 90编译器的任何计算机。操作系统：Linux，Windows，Mac。 RAM：取决于问题的复杂性。分类：4.11。问题性质：程序为各种奇异积分提供了高斯-勒根德尔和切比雪夫（Fejér-1）权重。求解方法：权重是从以下条件获得的：对于度≤（N-1）的多项式，阶N的正交必须精确。权重表示为与Legendre或Chebyshev多项式关联的奇异内核的矩。这些矩以适于计算的解析形式获得。附加说明：如果使用NAGWare f95编译器，则必须在Makefile的编译命令行中包含选项“ -kind = byte”。运行时间：发行版随附的测试运行需要花费几秒钟的时间来执行。

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