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Re: perturbation methods example from stephen lynch's book?

• To: mathgroup at smc.vnet.net
• Subject: [mg100775] Re: perturbation methods example from stephen lynch's book?
• From: sean_incali <sean_incali at yahoo.com>
• Date: Sat, 13 Jun 2009 06:05:37 -0400 (EDT)
• References: <h0nul6$bdd$1@smc.vnet.net> <h0sbmk$h6c$1@smc.vnet.net>

Hi Simon,

Thanks for the reply.

Actually I've found some resources on wolfram website.

http://library.wolfram.com/infocenter/MathSource/5269/

It seems like an excellent resource for those who wants to learn and
use asymptotics in mathematica. Only problem is that it uses
mathematica 3...

And Lynch's example 7 and typos come from his duffing equation.
Instead of x''+x+eps x^3 =0, he uses x''+x =eps x^3

Differences show in O(e) eqn.

o1 = DSolve[{x0[t] + x0''[t] == 0, x0'[0] == 0, x0[0] == 1 }, x0[t], t]
[[1, 1]]
DSolve[{x0[t]^3 + x1[t] + x1''[t] == 0 /. {x0[t] -> Cos[t]}, x1'[0] ==
0, x1[0] == 0 }, x1[t], t][[1, 1]]
oe = % // Simplify // Expand
"x~xp=" o1[[2]] + \[Epsilon] (oe)[[2]]
% // TraditionalForm


vs.

o1 = DSolve[{x0[t] + x0''[t] == 0, x0'[0] == 0, x0[0] == 1 }, x0[t], t]
[[1, 1]]
DSolve[{-x0[t]^3 + x1[t] + x1''[t] == 0 /. {x0[t] -> Cos[t]}, x1'[0]
== 0, x1[0] == 0 }, x1[t], t][[1, 1]]
oe = % // Simplify // Expand
"x~xp=" o1[[2]] + \[Epsilon] (oe)[[2]]
% // TraditionalForm