Numerical solution of differential equation with boundary
in [Mathematica]
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From: susy on 21 May 2010 06:43 It does not work for bc F[10^-5] == Pi Having searched using google for some time, I found a solution as follows: \[Epsilon] = 10^-10; fSky[sl_?NumericQ] := NDSolve[{(1/4 r^2 + 2 Sin[F[r]]^2) F''[r] + 1/2 r F'[r] + Sin[2 F[r]] ( F'[r])^2 - 1/4 Sin[2 F[r]] - 1/(r)^2 Sin[F[r]]^2 Sin[2 F[r]] == 0, F[\[Epsilon]] == \[Pi], F'[\[Epsilon]] == sl}, F, {r, \[Epsilon], 1000}] fSky2[sl_?NumericQ] := With[{f = fSky[sl][[1, 1, 2]]}, f[f[[1, 1, 2]]]] Plot[fSky2[sl], {sl, -5.468, -5.469}] Plot[Evaluate[F[r] /. fSky[sl /. sl -> -5.46877516]], {r, 0., 10}, PlotRange -> All, Frame -> True] It seems be able to give the correct result comparing with that given in some published paper. But the problem is that FindRoot[fSky2[sl] == 0, {sl, -5.}] cannot find a root, because the root probably does not exist. If we plot fSky2[sl] as shown in the above range, one may see a discontinuous ossilation around 0. Who can propose a better solution? Thanks in advance for your attention. |