# Solving numerically the equation of motion of D7 brane perturbation

+ 5 like - 0 dislike
83 views

I want to solve this equation

$$\partial_{\rho}^{2}\phi+\frac{3}{\rho}\partial_{\rho}\phi+\left(\frac{M^{2}}{(1+\rho^{2})^{2}}-\frac{l(l+2)}{\rho^{2}}\right)\phi=0$$

numerically.

I know that this equation can be transformed into the hypergeometric equation through the transformation $$\phi(\rho) = \rho^l (1+\rho^2)^{-\alpha} P(\rho)$$ (in which $P$ is some function) whose exact solution is the well known function see here $$_2 F_1(a,b;c;\rho) = \sum_{n=0}^\infty \frac{(a)_n (b)_n}{(c)_n} \frac{\rho^n}{n!}.$$

The crucial characteristic of this function is that if $a$ or $b$ are negative integers, then the series is finite.

However, I'm interested in exploring a numerical solution for this equation and I would like to know how to obtain numerically the finite series solutions.

Any idea?

Thanks.

This post imported from StackExchange Mathematics at 2015-05-09 14:49 (UTC), posted by SE-user miguelFe
retagged May 9, 2015
You might want to try Math SE. Take a look at the non-linear example here: en.wikipedia.org/wiki/…

This post imported from StackExchange Mathematics at 2015-05-09 14:49 (UTC), posted by SE-user user6972
You might be able to identify the form/solution with this book books.google.com/…

This post imported from StackExchange Mathematics at 2015-05-09 14:49 (UTC), posted by SE-user user6972
To clarify, $\phi = \phi(\rho)$? On what interval do you wish to solve the D.E.? What restraints do you have on $M$ and $l$?

This post imported from StackExchange Mathematics at 2015-05-09 14:49 (UTC), posted by SE-user Kyle

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysic$\varnothing$OverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.