Numerical integration - Gauss Lobatto

1. The problem statement, all variables and given/known data
I need calculate the points (##x_i##) and weights (##w_i##) with Gauss Lobatto seven points on the interval [a,b]. With the points and the weights I am going to approximate any integral at this interval.


2. Relevant equations
I have found the relevant points and weights at the interval [-1,1] using tables etc (https://www.math.ntnu.no/emner/TMA4125/2019v/notater/tabell_gauss.pdf)


3. The attempt at a solution
If I could adjust ##x_i## and ##w_i## from the interval [-1,1] to [a,b] with a linear transformation, I think the problem would be solved. But I have only found the values, and can't find a general formula for ##x_i## and ##w_i##.

Thanks
 

Ray Vickson

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1. The problem statement, all variables and given/known data
I need calculate the points (##x_i##) and weights (##w_i##) with Gauss Lobatto seven points on the interval [a,b]. With the points and the weights I am going to approximate any integral at this interval.


2. Relevant equations
I have found the relevant points and weights at the interval [-1,1] using tables etc (https://www.math.ntnu.no/emner/TMA4125/2019v/notater/tabell_gauss.pdf)


3. The attempt at a solution
If I could adjust ##x_i## and ##w_i## from the interval [-1,1] to [a,b] with a linear transformation, I think the problem would be solved. But I have only found the values, and can't find a general formula for ##x_i## and ##w_i##.

Thanks
Convert your integral ##\int_a^b f(x) \, dx## into ##\int_{-1}^1 c f(r+cy) \, dy##. Apply Gauss-Lobato to the latter, then invert the transformation to get the correct formula for your original problem.
 

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