# Questions tagged [collocation]

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15 questions
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### Non-hermitian discretizations in quantum mechanics

Consider the Schroedinger equation $$\left(-\frac12\frac{\partial^2}{\partial x^2} + V(x) \right) \psi(x) = E \psi(x)$$ The usual way to solve it is to introduce a discretization of $\psi(x)$. This ...
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### Numerically inverting an exponentially growing function (defined by Chebyshev polynomials)

Assume a function $M(t)$ strictly increasing, essentially growing exponentially, and asymptoptically growing at a known rate $\bar{g}$, i.e. $\lim_{t\to\infty}M'(t)/M(t) = \bar{g}$ In a set of awful ...
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### Does anyone have a driver for fortran DAE solver - COLDAE?

Coldae is a solver writter by U Ascher and R Spiteri, located here http://www.cs.ubc.ca/~ascher/coldae.f . It can solve upto index-2 DAEs using collocation. I am new to Fortran, and having a hard ...
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### Motivation behind Collocation Method

In previous question "Motivation behind Galerkin method", Paul gives a good and easy-understanding explanation indicating that the Galerkin method is a kind of projection method. Can anyone explain ...
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### Second and Higher Order Order Corrector in Spectral Deferred Correction

I am trying to work out a second order or higher order correction for the method of Spectral deferred Correction (SDC). Specifically using as a corrector a second order or third order multi-step. In ...
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### Spectral Methods in time

I was reading up on Spectral Methods for PDEs. In all the descriptions I read, while the position component is approximated via a Fourier series or other methods, the time component is still ...
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### How do I perform chebyshev interpolation from a to b with custom angle range?

Typically Chebyshev interpolation from $-1$ to $1$ with angle from $0$ to $\pi$: $\xi_j=\cos \left ({\pi j \over N}\right )$ $x_j=(1+\xi_j) * {L \over 2}$ $w$: $w_0=\pi/(2N)$ $w_{1,...,N-1}=\pi/(N)$...
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### Sparse matrices origins

I am using the sparse matrices provided by the University of Florida Sparse Matrix Collection and most matrices are accompanied with little description of the problem or discipline from which the ...
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### Stochastic Collocation for time evolving ODE

For an Stochastic Differential Equation, e.g., $$\frac{du}{dt} = \alpha*\sin(u*t)$$ where $\alpha$ is normally distributed with nonzero mean, I am trying to use a stochastic collocation approach ...