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NDSolve: ..numerically ill-conditioned...

• To: mathgroup at smc.vnet.net
• Subject: [mg109474] NDSolve: ..numerically ill-conditioned...
• From: Alessio Giberti <giberti at fe.infn.it>
• Date: Wed, 28 Apr 2010 07:00:07 -0400 (EDT)

I have to solve numerically equations like

u''[x] - 1*^7 u[x] ==  3.6*^7,
u'[0]==0, u'[2*^-3]==0,

but I get the message:

"The equations derived from the boundary conditions are numerically 
ill-conditioned. The boundary conditions may not be sufficient to 
uniquely define a solution. The computed solution may match the boundary 
conditions poorly."

No problem with less extreme coefficients, the solutions are good, but 
more extreme coefficients lead to non-reliable results. What can I do to 
overcome the problem?