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Apr
6
comment Perturbation theory PDEs
I would argue this was not your original post.
Mar
29
revised Maclaurin series and general terms
minor typo in title
Mar
29
suggested suggested edit on Maclaurin series and general terms
Mar
27
comment Perturbation theory PDEs
If you apply the above procedure iteratively n times it will provide you with a solution up to order ϵ^n. What would be a converged solution in your view? Compared to a numerical solution?
Mar
27
comment Perturbation theory PDEs
It obeys the original equation at order ϵ^2 so that is more or less the definition of a perturbative solution. Note that the method would also work for the full blown problem of Ψ(r,t,p) it would just be more messy.
Mar
27
awarded  Teacher
Mar
26
comment Perturbation theory PDEs
@Lipschitz could you please explain to me why my answer is not answering your question?
Mar
23
revised Perturbation theory PDEs
added 63 characters in body
Mar
23
revised Perturbation theory PDEs
deleted 10 characters in body
Mar
23
answered Perturbation theory PDEs
Mar
23
comment Perturbation theory PDEs
@Lipschitz it is rigorous! At least for a physicist :-)
Mar
23
awarded  Commentator
Mar
23
comment Perturbation theory PDEs
But your question claims actual solution is known, so I it is fair to assume the square is known too?
Mar
23
comment Perturbation theory PDEs
Naively (as a physicist), one would write $\Psi=\Psi_0+\epsilon \Psi_1$. Replace in original equation assuming $\Psi_0$ solves original equation. Get a new (linear) equation for $\Psi_1$ involving r.h.s. with (known) $\Psi_0^2$… iterate?
Sep
17
comment Evaluate $\int_1^\infty \cosh^{-1}(x) \ln(x^2-1) \exp \left(- \frac{x}{T} \right) dx $
Thanks! Very impressive! FYI this computation was needed for this paper fr.arxiv.org/pdf/1211.7352 for which we gave up presenting the corresponding anisotropic closed form.
Sep
17
accepted Evaluate $\int_1^\infty \cosh^{-1}(x) \ln(x^2-1) \exp \left(- \frac{x}{T} \right) dx $
Dec
15
comment Change of variables in Belousov-Zhabotinsky reaction
Could you please change you title to something more specific? Thanks
Nov
27
revised Definite integral over triple products of higher order Bessel functions.
added 204 characters in body
Nov
27
comment Definite integral over triple products of higher order Bessel functions.
@Phira thanks for the advice; it seems difficult to do in practice since 3 such functions are involved??
Nov
27
asked Definite integral over triple products of higher order Bessel functions.