NDsolve problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg110699] NDsolve problem*From*: "ntina.86 at libero.it" <ntina.86 at libero.it>*Date*: Fri, 2 Jul 2010 07:27:30 -0400 (EDT)*Reply-to*: "ntina.86 at libero.it" <ntina.86 at libero.it>

Hello, I haven't been using Mathematica for some years and now I need to ask you for help with NDSolve. I'm using version 6.0. I want to solve the radial Schrodinger equation with a Yukawa potential, and I started trying to solve this: a = 500 b = 10; s = NDSolve[{y''[x] + (2/x) y'[x] + (1 + (2*a/x)*E^(-b*x)) (y[x]) == 0, y [0.000001] == 1, y'[0.000001] == -a}, y, {x, 0.000001, 60},PrecisionGoal -> \ [Infinity], MaxSteps -> Infinity] This gives me results that might be correct, but the problem comes when I try to plot: Plot[Evaluate[(x*y[x])^2 + (((x - 0.5 Pi)*y[x - 0.5 Pi]))^2 /.s[[1]]], {x, 10, 60}, PlotRange -> All] It should be a constant (i.e. the sum of the square of a cosine and of a sine, which is the solution of the Schrod.) at least for x>10, instead I get a badly oscillating function. Is it a problem of the method of integration or I'm doing something wrong? I tried to change it, using ExplicitRK or the SymplecticPartitionedRK, but the latter gives me these errors: --------------------------------------------------------------------------------------------------------- NDSolve::nlnum1: The function value {-21065.3 (1.23594*10^7+82.8327 \ TemporaryVariable[2][1.1462*10^-6])} is not a list of numbers with \ dimensions {1} when the arguments are {1.1462*10^-6,0.494377}. InterpolatingFunction::dmval: Input value {28.4292} lies outside the \ range of data in the interpolating function. Extrapolation will be \ used. >> InterpolatingFunction::dmval: Input value {30} lies outside the range \ of data in the interpolating function. Extrapolation will be used. >> NDSolve::nlnum1: The function value {-21193.5 (1.23496*10^7+82.3232 \ TemporaryVariable[2][1.14631*10^-6])} is not a list of numbers with \ dimensions {1} when the arguments are {1.14631*10^-6,0.493983}. InterpolatingFunction::dmval: Input value {28.4292} lies outside the \ range of data in the interpolating function. Extrapolation will be \ used. >> General::stop: Further output of InterpolatingFunction::dmval will be \ suppressed during this calculation. >> NDSolve::nlnum1: The function value {-21321.9 (1.23397*10^7+81.8195 \ TemporaryVariable[2][1.14643*10^-6])} is not a list of numbers with \ dimensions {1} when the arguments are {1.14643*10^-6,0.493589}. General::stop: Further output of NDSolve::nlnum1 will be suppressed \ during this calculation. >> ------------------------------------------------------------------------------------------------------- Thank you in advance. Regards, Valentina