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NDSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125236] NDSolve
  • From: rf248 <rf248 at st-andrews.ac.uk>
  • Date: Thu, 1 Mar 2012 05:34:47 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello,
I am trying to solve an initial value problem with NDSolve. However, the initial values are set on a regular singular point. When solving Bessel's differential equation, one can avoid this problem with the option SolveDelayed ->True.
This however does not help with the following problem (hydrogen atom) to which the analytic solution is a Laguerre polynomial.

l = 0; n = 1; a = 1; eps = -1/(2 n^2);
func = r D[r R[r], {r, 2}] + (2 (a r + eps r^2) - l (l + 1)) R[r] == 0;
nrad = NDSolve[{func, R[0] == 2, R'[0] == -2}, R[r], {r, 0, 100}, 
  SolveDelayed -> True]

Above, the initial values chosen correspond to an exact solution for constants l, n, a and eps. Mathematica must therefor be able to find a solution.

Thanks!



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