% Program to get the quadrature points

% and weight for Gauss-Legendre Quadrature

% Rule

clc

clear all

syms x

% Input n: Quad pt rule

n=14;

% Calculating the Pn(x)

% Legendre Polynomial

% Using recursive relationship

% P(order of polynomial, value of x)

% P(0,x)=1; P(1,x)=0;

% (i+1)*P(i+1,x)=(2*i+1)*x*P(i,x)-i*P(i-1,x)

m=n-1;

P0=1;

P1=x;

for i=1:1:m

Pn=((2.0*i+1)*x*P1-i*P0)/(i+1.0);

P0=P1;

P1=Pn;

end

if n==1

Pn=P1;

end

Pn=expand(Pn);

quadpts=solve(vpa(Pn,32));

quadpts=sort(quadpts);

% Finding the weights

% Formula for weights is given at

% http://mathworld.wolfram.com/Legendre-GaussQuadrature.html

% Equation (13)

for k=1:1:n

P0=1;

P1=x;

m=n;

% Calculating P(n+1,x)

for i=1:1:m

Pn=((2.0*i+1)*x*P1-i*P0)/(i+1.0);

P0=P1;

P1=Pn;

end

Pn=P1;

weights(k)=vpa(2*(1-quadpts(k)^2)/(n+1)^2/ …

subs(Pn,x,quadpts(k))^2,32);

end

fprintf(‘Quad point rule for n=%g \n’,n)

disp(‘ ‘)

disp(‘Abscissas’)

disp(quadpts)

disp(‘ ‘)

disp(‘Weights’)

disp(weights’)_______________________________________________________

# A MATLAB program to find quadrature points and weights for Gauss-Legendre Quadrature rule

Recently, I got a request how one can find the quadrature and weights of a Gauss-Legendre quadrature rule for large n. It seems that the internet has these points available free of charge only up to n=12. Below is the MATLAB program that finds these values for any n. I tried the program for n=25 and it gave results in a minute or so. The results output up to 32 significant digits.

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I wrote something similar, using mathematica instead, after watching your videos on applying the Gauss quadrature rules. I decided to offer the tabulated result on the page, too, in case it turns out to be useful for people who just want the quick values, with a download for the high precision numbers. Perhaps of interest, it’s up on http://processingjs.nihongoresources.com/bezierinfo/legendre-gauss-values.php (I used it as a resource for computing the arc length integral using legendre-gauss approximation, for http://processingjs.nihongoresources.com/bezierinf)

I wrote something similar, using mathematica instead, after watching your videos on applying the Gauss quadrature rules. I decided to offer the tabulated result on the page, too, in case it turns out to be useful for people who just want the quick values, with a download for the high precision numbers. Perhaps of interest, it’s up on http://processingjs.nihongoresources.com/bezierinfo/legendre-gauss-values.php (I used it as a resource for computing the arc length integral using legendre-gauss approximation, for http://processingjs.nihongoresources.com/bezierinf)

Thank you. This would be very useful to many people out there.

Mr Kamermans’ tables are indeed useful. Now I can make hats!

Mr Kamermans’ tables are indeed useful. Now I can make hats!

Sir kindly send me source code in MAT LAB for gaussian quadrature formula where [-1,1] is mapped into [0,1]

Sir kindly send me source code in MAT LAB for gaussian quadrature formula where [-1,1] is mapped into [0,1]

thank you so much for this! 🙂

thank you so much for this! 🙂

plz can someone send me matlab codes for guassion quadrature

plz can someone send me matlab codes for guassion quadrature

Outstanding. This works perfectly. Thank you!

Outstanding. This works perfectly. Thank you!