# 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 LegendreChebyshev 1stChebyshev 2ndLaguerreHermiteJacobiLobattoKronrod order n 23456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100 α β 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
Nodes and Weights of Gaussian quadrature (Select method)
 [1-10] /26 Disp-Num5103050100200
[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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