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Coupled second-order nonlinear ODEs

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90475] Coupled second-order nonlinear ODEs
  • From: dkjk at bigpond.net.au
  • Date: Thu, 10 Jul 2008 06:36:57 -0400 (EDT)

Hi all,

I'm trying to solve the following system

\[Lambda]1 = 1;
\[Lambda]2 = 1;
M = 1;
v = 1;
h = 1;
m = 20;
s = NDSolve[{-1/2 (-M^2 + h \[Eta][y]^2) \[CurlyPhi][y] -
     2 \[Lambda]1 \[CurlyPhi][y]^3 + \[CurlyPhi]''[y] ==
    0, -4 \[Eta][y] (-v^2 + \[Eta][y]^2) \[Lambda]2 -
     h \[Eta][y] \[CurlyPhi][y]^2 + \[Eta]''[y] == 0, \[Eta][0] ==
    0, \[Eta]'[0] == 1, \[CurlyPhi][0] == 1, \[CurlyPhi]'[0] ==
    0}, {\[Eta], \[CurlyPhi]}, {y, -m, m}, WorkingPrecision -> 20]
Plot[\[CurlyPhi][y] /. s, {y, -m, m}]
Plot[\[Eta][y] /. s, {y, -m, m}]

but keep running into the error ``step size is effectively zero;
singularity or stiff system suspected''.  I tried increasing
WorkingPrecision to no avail.  Can anyone please advise if Mathematica
is able to solve this?

Best regards,
James


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