A question about numerically solving differential equations
- To: mathgroup at smc.vnet.net
- Subject: [mg130242] A question about numerically solving differential equations
- From: Yue Zhao <zhaoyue.hep at gmail.com>
- Date: Tue, 26 Mar 2013 04:06:10 -0400 (EDT)
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Hi,
I am using Mathematica to numercially solve the following equations:
2 D[f0[r], r]/r + D[f0[r], r, r] == -2 A f1[r]/r^4 + 2 A D[f1[r], r]/r^3
-2 f1[r]/r^2 + 2 D[f1[r], r]/r + D[f1[r], r, r] == 2 A D[f0[r], r]/r^3
And my boundary condition is
f0[10] == 0.01, f1[10] == 0.01, (D[f0[r], r] /. r -> 1) == 10^-3 A,
(D[f1[r], r] /. r -> 1) == 0
When I take A to be small, say 1, everything is fine. However, if I take A to be large, e.g. 100. Mathematica complains and gives me crazy results. Here are the error message I get:
NDSolve::bvluc: 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. >>
NDSolve::berr: There are significant errors {-5.55116*10^6,-7.26312*10^6,0.,0.} in the boundary value residuals. Returning the best solution found. >>
Can anyone help me to deal with this issue? I appreciate your help!
Thanks!
YZ