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numerical integration - What do these error messages mean when numerically solving differential equations?


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!





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