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- 05/25/14--03:40: _how to solve by vim...
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- 05/28/16--02:31: _Problem with HPM
- 06/16/16--19:59: _ Metric Perturbation
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- 05/25/14--03:40: _how to solve by vim...
- 03/23/18--13:41: _perturbation theorie
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## Channel Description:

hi dears. i cant solve this question by Analytical method such variational itteration method (VIM) or homotopy perturbation method (HPM), homotopy analysis method(HAM)

Hello everyone,

I've been trying to do some perturbation theory and ran into some problems I don't quite understand. I implemented the Hamiltonian of the Bose-Hubbard model and treated the hopping as a perturbation. Calculating the second order energy shift is easily accomplished, but when I'm only interested in one of the two occuring terms, I run into problems. The calculation takes minutes to finally fail, giving me an "too many levels of recursion"-error. I need to be able to just pick a few terms for some calculations, I'm doing, and can't figure out what I might be doing wrong. Here is the source code (download is below):

Download too_many_levels_of_recursion.mw

It would be great, if someone could point out the mistake, I'm making. I copy/pasted the last line, so there shouldn't be any typos.

Thanks in advance,

Sören

Hi!

I seem to run into problems with (quantum) perturbation theory. In the following minimal working example, an energy denominator, as occuring in perturbation theory is not evaluated if I previously assume that the quantum number is a positive integer. It's supposed to return an error, as the energy denominator is 0.

Download energy_denominator.mw

Best regards,

Sören

HPM_4.mwhi, I am using homotopy perturbation technique but there is arising an error in comaring coeffecient of p^0, p^1,.... plz help me

Hi everyone.

I'm going to solve a problem with HPM in Maple. I wrote some initial codes but now I'm confused becouse of P^0 coefficients in A1 and B1. I mean I can't reach to f0 and g0.

I upload that file. these are codes that i typed. could you please help me how can I reach to them(f0 & g0)?

http://www.filehosting.org/file/details/573095/Maple%20Project+.mw

Hi All,

I'm using the Physics package, which enables GR calculations, ie defining metrics and tensor algebra.

Was just curious if it were possible to add a perturbation to the metric when calculating Ricci and Christoffels.

I would like something like

g_[] = g1_[mu,nu] + h[mu,nu]

And then do a calculation like,

Ricci[].

I know this would be possible if I define everything and re-write the calculations for calculating Ricci, i.e

Define(g1[mu,nu], h[mu,nu]);

and the proceed with GR calculations to find Ricci, however was hoping there was an easier way to do this.

Any help is appreciated.

Thanks guys.

Please help me to solve the system of 1st order singular O.D.E (see uploaded file)....New_Microsoft_Office_Word_Document.docx

hi dears. i cant solve this question by Analytical method such variational itteration method (VIM) or homotopy perturbation method (HPM), homotopy analysis method(HAM)

Hi all, I am having the follwing DE:

restart:

(diff(z(x), x, x))-z(x) - cos(2*x)/(1+delta*z(x)) = 0:

With initial conditions: z(-pi/4)=z(pi/4)=0 and |delta|<<1

I showed **by hand** by using perturbation theory the second order approximation. The hint was: you can use Maple to check your answer.

Is there somebody who can help me with this?

0 | 0 |

I am working with the following differential equation:

$\frac{d^2z}{dx^2}+z=\frac{\cos 2x}{1+\epsilon z},\:\:\:z(-\pi/4)=z(\pi/4)=0$

where modulus of $\epsilon$ is much less than $1$. The task is then to use perturbation theory (with Maple, if necessary) to show that the second-order approximation to the solution to this DE is:

$z=-\frac{1}{3}\cos 2x +\epsilon\bigg(\frac{1}{6}-\frac{8\sqrt{2}}{45}\cos x - \frac{1}{90}\cos 4x \bigg) + \epsilon^2 \bigg(\frac{2\sqrt{2}x}{45}\sin x - \frac{\sqrt{2}}{90}(\pi + 1)\cos x + \frac{7}{720} \cos 2x - \frac{\sqrt{2}}{90}\cos 3x - \frac{1}{1050}\cos 6x \bigg).$

I will then likely have to use Maple to determine the third-order term $\delta^{3}z_{3}(x)$ and evaluate $z_{3}(x)$ at $x=0$ and $x-\pi/8$.

My starting point is to use the theory for a regular perturbation (since the modulus of $\epsilon$ is much less than $1$). For the unperturbed equation, I could set $\epsilon=0$ as that would give a simple differential equation which should be solvable. I can then see that $1/{1+\epsilon z}$ can be expanded to second-order in $\epsilon$ as $1 - \epsilon z + \epsilon^2 z^2 + O(\epsilon^3), which looks promising. Could someone advise how I put this together? Do I then have to multiply the unperturbed solution by the expansion in $\epsilon$?

Dear sir / madam

Hi

I'm a student of mechanical engineering and looking for some HPM ( homotopy perturbation method) maple codes with the related article to practice more in this field.

can I ask you for help?

unfortunately, I couldn't find any articles with maple solution about HPM.

sincerely

Aidin