SageManifold solving differential equations (Schwarzschild metric)

asked 2015-08-08 08:08:26 +0100

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I've been following Schwarzschild derivation here https://en.wikipedia.org/wiki/Derivin... and I've come to the point where I have the three differential equations listed in the above link.

I tried to solve it with

desolve_system

as follows: https://www.dropbox.com/s/1uihjhzm2k1...

But it does not seem to be working. Am I missing something? It's a system of nonlinear differential equations

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answered 2015-08-08 18:29:10 +0100

eric_g
8469 ●10 ●62 ●168 https://luth.obspm.fr/...

Hi,

Your derivation seems OK to me. In particular, you get a system of differential equations equivalent to that listed in the Wikipedia page that you mention (modulo the change of notation A --> B, B --> A). The issue seems to be that Sage (actually Maxima) does not know how to solve this non-linear system, since you get the message:

ECL says: Error executing code in Maxima: desolve: can’t handle this case

Maybe you should try to simplify the system, as suggested in the Wikipedia page: adding the first two equations gives a simple equation: A B' - A' B = 0. Try then desolve with this equation and the third equation.

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Asked: 2015-08-08 08:08:26 +0100

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Last updated: Aug 08 '15

SageManifold solving differential equations (Schwarzschild metric) edit

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