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