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Finding Converging Function

• To: mathgroup at smc.vnet.net
• Subject: [mg125342] Finding Converging Function
• From: rf248 <rf248 at st-andrews.ac.uk>
• Date: Thu, 8 Mar 2012 04:37:15 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello!
I have found a solution to a function (e.g. the radial function of hydrogen) using NDSolve and would now like to vary a parameter such that the function converges to zero at infinity.
I am thinking of writing an iterative process that imposes convergence conditions.
Can Mathematica do this for me in an easier way? Or, is it maybe even possible to impose convergence to my function in NDSolve?

Here's an example:
The function is bound when a=-1/18

eps = $MachineEpsilon;
a = -0.055;
func = r D[r R[r], {r, 2}] + (2 (r + a r^2) - 2) R[r] == 0;
nrad = NDSolve[{func, R[eps] == 0, R'[eps] == 1}, 
  R[r], {r, eps, 100}]
Plot[R[r] /. nrad, {r, 0, 100}, PlotRange -> {{0, 50}, {-0.15, 0.3}}]

Thanks!!