- #1
confused_engineer
- 39
- 2
- TL;DR Summary
- I need to calculate the roots of the Chebyshev polynomials, but the results do not correspond with the theory
Hello everyone. I am trying to construct an optimization problem using Chebyshev pseudospectral method as described in this article. For that, I need to calculate the zeros of the Chebyshev polynomial of any order. In the article is sugested to do it as
tk=cos(πk/N) k=0, ..., N
However, if I assign the value 2 to N, the nodes are -1, 0 and 1.
The Chebyshev polynomial of order 3 is 4t3-3t and it's roots are -√3/2, 0 and √3/2, this doesn't correspond with the results of the expression above.
In my model I am using the first expression, the cosine, to find the collocation points instead of using the roots of the polynomial of order N. The solver returns an error or an incorrect optimal solution based on the number of colocation points. Can someone please tell me if I am doing it right by choosing my collocation points as the cosine or if I should try to find the roots of the polynomials instead?
Any answer is appreciated.
Thanks for reading.
Regards.
tk=cos(πk/N) k=0, ..., N
However, if I assign the value 2 to N, the nodes are -1, 0 and 1.
The Chebyshev polynomial of order 3 is 4t3-3t and it's roots are -√3/2, 0 and √3/2, this doesn't correspond with the results of the expression above.
In my model I am using the first expression, the cosine, to find the collocation points instead of using the roots of the polynomial of order N. The solver returns an error or an incorrect optimal solution based on the number of colocation points. Can someone please tell me if I am doing it right by choosing my collocation points as the cosine or if I should try to find the roots of the polynomials instead?
Any answer is appreciated.
Thanks for reading.
Regards.