Re: NDSolve: ..numerically ill-conditioned...
- To: mathgroup at smc.vnet.net
- Subject: [mg109481] Re: NDSolve: ..numerically ill-conditioned...
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Thu, 29 Apr 2010 02:53:04 -0400 (EDT)
Use exact numbers and DSolve or use higher precision with NDSolve eqns = {u''[x] - 1*^7 u[x] == 36*^6, u'[0] == 0, u'[2*^-3] == 0}; soln = DSolve[eqns, u[x], x][[1]] {u[x] -> -(18/5)} eqns2 = {u''[x] - 1*^7 u[x] == 3.6`35*^7, u'[0] == 0, u'[2*^-3] == 0}; soln2 = NDSolve[eqns2, u, {x, 0, 5}, WorkingPrecision -> 35][[1]]; Table[u[x] /. soln2, {x, 0, 5, .5}] {-3.6,-3.6,-3.6,-3.6,-3.6,-3.6,-3.6,-3.6,-3.6,-3.6,-3.6} Plot[Evaluate[u[x] /. soln2], {x, 0, 5}] Bob Hanlon ---- Alessio Giberti <giberti at fe.infn.it> wrote: ============= 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?