Nodes and Weights of Gaussian quadrature (Select method) Calculator

Calculates the nodes and weights of the Gaussian quadrature.
(i.e. Gauss-Legendre, Gauss-Chebyshev 1st, Gauss-Chebyshev 2nd, Gauss-Laguerre, Gauss-Hermite, Gauss-Jacobi, Gauss-Lobatto and Gauss-Kronrod)

kinds
order n
α
β

    Nodes and Weights of Gaussian quadrature (Select method)
    [1-10] /26Disp-Num
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    [1]  2022/09/24 02:32   60 years old level or over / A retired person / Very /
    Purpose of use
    Developing a textbook
    [2]  2022/02/11 12:33   60 years old level or over / A retired person / Very /
    Purpose of use
    Researching a new statistical test. Checking how few terms and thus how accurately and how fast I can calculate.

    Gaussian quadrature is not taught and is almost unknown in Australia. My interest was provoked by a maths problem within a science research task (forces between magnets) by two 15-year old boys. For the simplified problem, we re-invented Gauss-Legendre quadrature. This was good fun and good experience for them! We created a new weighting function, solved for the weights and abscissae, and reduced a horrible two dimensional integral needing a vast set of points down to a one dimensional integral needing only a few points. Then I noticed the problem could be "folded in half" and added, which required only Gauss-Jacobi quadrature, for which the abscissae and weights are already known.

    I know people and have read papers using GQ for a range of research projects in Namibia, Nigeria, South Africa, ... Interesting thoughts occur about my assumptions and prejudices.
    [3]  2019/05/21 16:42   Under 20 years old / High-school/ University/ Grad student / Very /
    Purpose of use
    Research/Assignment
    [4]  2019/05/14 06:11   20 years old level / A teacher / A researcher / Very /
    Purpose of use
    Research
    [5]  2019/03/27 12:32   20 years old level / Elementary school/ Junior high-school student / Useful /
    Purpose of use
    calculation
    [6]  2019/01/17 18:09   60 years old level or over / A teacher / A researcher / Very /
    Purpose of use
    research (kinetic modelling)
    [7]  2018/11/26 15:03   30 years old level / High-school/ University/ Grad student / Very /
    Purpose of use
    project
    Comment/Request
    good service
    [8]  2018/09/10 12:51   30 years old level / High-school/ University/ Grad student / Very /
    Purpose of use
    Implementation of orthogonal collocation
    [9]  2018/07/28 03:44   20 years old level / An engineer / Useful /
    Purpose of use
    Building custom FEA codes. Need to implement Gaussian quadrature to evaluate element matrices, which involves integrating a constitutive matrix transformed to a shape function basis.
    Comment/Request
    In addition to the numerical values, analytical solutions would be nice to have. Maybe not for a production code, but very useful for more sophisticated prototyping and playing with ideas.
    [10]  2018/07/13 08:48   40 years old level / A teacher / A researcher / Very /
    Purpose of use
    Scientific publications, Ill cite this website.

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