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Jun
13 |
comment |
Rigorous results on the method of multiple scales
Thank you, Jon, I'll check this out. |
Jun
7 |
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Rigorous results on the method of multiple scales
Jon, I've looked at p.360 and the following calculations but I did not see a theorem, if you meant that it should be possible to prove a theorem using the calculations in those pages, I am actually looking for a source where this is done. As for the two-scale approach being "well-supported by the adiabatic approximation", I'm not sure whether you are making a plausibility argument or claiming it should be possible to give proofs along those lines. If it is the latter case, once again, I would love to see a book/paper where this is done. |
Jun
4 |
awarded | Scholar |
Jun
4 |
comment |
Rigorous results on the method of multiple scales
Thank you, Aleksey. |
Jun
4 |
accepted | Perturbation theory for the generalized eigenvalue problem |
Jun
4 |
comment |
Rigorous results on the method of multiple scales
Thanks, Jon. I did a quick scan of Kevorkian and Cole and did not immediately see theorems of the sort I've mentioned (i.e. guarantees of accuracy). Do they have such theorems in the book? |
Jun
4 |
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Perturbation theory for the generalized eigenvalue problem
Thanks, Robert, that was an eye-opener. |
Jun
4 |
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Perturbation theory for the generalized eigenvalue problem
Various nice properties (e.g., orthogonality) of the eigenvectors follow easily from the Hermiticity of $A$ and $B$, and I was hoping that the perturbation theory would be better-behaved in this form. The general theory of perturbations of eigenvalues (of a possibly non-normal matrix, which $B^{-1}A$ may be) seemed a little scary, but maybe it will turn out to be ok, and I may end up trying that. The case of positive-definite $B$ was an almost trivial generalization of the usual perturbation theory for a Hermitian matrix with all the usual niceties, so I was hoping to have something similar. |
Jun
4 |
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Rigorous results on the method of multiple scales
@Steve Huntsman, I had read parts of Barenblatt's book years ago (I remember it as a fun and insightful book), does it have a discussion of the method of multiple scales, or did you cite it as a reference of general relevance along these lines? |
Jun
4 |
asked | Rigorous results on the method of multiple scales |
Jun
4 |
asked | Perturbation theory for the generalized eigenvalue problem |
Feb
9 |
awarded | Commentator |
Feb
9 |
comment |
Rolling without slipping interpretation of torsion
David, do you know of a reference for a rigorous version (and proof) of the statement you give? (A semi-rigorous proof would also be helpful.) |
Oct
28 |
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Oct
28 |
revised |
Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature
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