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Results tagged with collocation
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user 9692
0
votes
3
answers
558
views
Calculating integrals for a function approximated by Chebyshev polynomials
Setup (complete, but all very standard):
My problem is how to best calculate the cumulative integral of a function which comes out of Spectral Collocation with a chebyshev basis. … end{align}
Which gives the complete set of integrals as,
$$
\vec{F} =\Omega \cdot (\vec{f}(0:N) + \vec{f}(1:N+1))\in\mathbb{R}^{N+2}
$$
This is especially useful for me because I am solving a spectral collocation …
- 376
1
vote
0
answers
48
views
Numerically inverting an exponentially growing function (defined by Chebyshev polynomials)
The function $M(t)$ will be solved numerically with some sort of spectral collocation method with a polynomial basis (see below). … find the appropriate $M$, and then use some sort of interpolation to find the approximating $q(M)$, but I would prefer an approach that has a chance of using auto-differentiation by throwing it into my collocation …
- 376