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