ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 08 Aug 2015 18:29:10 +0200SageManifold solving differential equations (Schwarzschild metric)https://ask.sagemath.org/question/28774/sagemanifold-solving-differential-equations-schwarzschild-metric/ Hi
I've been following Schwarzschild derivation here https://en.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution#Using_the_field_equations_to_find_A.28r.29_and_B.28r.29 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/1uihjhzm2k1wl4a/2015-08-07-133804.pdf?dl=0
But it does not seem to be working. Am I missing something? It's a system of nonlinear differential equationsSat, 08 Aug 2015 08:08:26 +0200https://ask.sagemath.org/question/28774/sagemanifold-solving-differential-equations-schwarzschild-metric/Answer by eric_g for <p>Hi</p>
<p>I've been following Schwarzschild derivation here <a href="https://en.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution#Using_the_field_equations_to_find_A.28r.29_and_B.28r.29">https://en.wikipedia.org/wiki/Derivin...</a> and I've come to the point where I have the three differential equations listed in the above link.</p>
<p>I tried to solve it with </p>
<blockquote>
<p>desolve_system</p>
</blockquote>
<p>as follows:
<a href="https://www.dropbox.com/s/1uihjhzm2k1wl4a/2015-08-07-133804.pdf?dl=0">https://www.dropbox.com/s/1uihjhzm2k1...</a></p>
<p>But it does not seem to be working. Am I missing something? It's a system of nonlinear differential equations</p>
https://ask.sagemath.org/question/28774/sagemanifold-solving-differential-equations-schwarzschild-metric/?answer=28781#post-id-28781Hi,
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: canâ€™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.
Sat, 08 Aug 2015 18:29:10 +0200https://ask.sagemath.org/question/28774/sagemanifold-solving-differential-equations-schwarzschild-metric/?answer=28781#post-id-28781