NDSolve for BVP: Increasing MaxIterations, reverse direction

*To*: mathgroup at smc.vnet.net*Subject*: [mg124250] NDSolve for BVP: Increasing MaxIterations, reverse direction*From*: gac <g.crlsn at gmail.com>*Date*: Sat, 14 Jan 2012 17:11:06 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

I am trying to solve a boundary value problem with NDSolve. I have two questions: 1. How do I increase MaxIterations? 2. Can I reverse the direction of integration of NDSolve? My Mathematica 8 notebook to solve the modified spherical Bessel equation is appended below. I am comparing the NDSolve solution to the exact solution BesselI[2,r]/Sqrt[r]. In fact, for this exercise, I'm trying to force NDSolve to give me the exact solution. I also include a parameter sigma that should evaluate to 1. I can't seem to get around the error message: "FindRoot::cvmit: Failed to converge to the requested accuracy or precision within 100 iterations." How do I increase MaxIterations in NDSolve? Also, I think I might get a better result if NDSolve would integrate from rEnd to r0 instead of r0 to rEnd. Can I specify that NDSolve should solve the problem in the reverse direction? Thanks very much. gac rTiny = 10^-12; r0 = rTiny; rEnd = 1; \[Phi]Exact[r_] := Sqrt[Pi/(2 r)] BesselI[2, r]; \[Phi]0 = \[Phi]Exact[r0]; \[Phi]p0 = D[\[Phi]Exact[r], r] /. r -> r0; \[Phi]End = \[Phi]Exact[rEnd]; sol = NDSolve[{r^2 \[Phi]''[r] + 2 r \[Phi]'[r] - r^2 \[Phi][r] == 2 \[Sigma][r] \[Phi][r], \[Sigma]'[r] == 0, \[Phi][r0] == \[Phi]0, \[Phi]'[r0] == \[Phi]p0, \[Phi][rEnd] == \[Phi]End}, {\[Phi], \[Sigma]}, r, WorkingPrecision -> 20]; Plot[{\[Phi][r] /. First[sol], \[Phi]Exact[r]}, {r, 0, rEnd}, PlotStyle -> {Red, Blue}] \[Sigma][0] /. First[sol]