       Re: NDsolve problem

• To: mathgroup at smc.vnet.net
• Subject: [mg110729] Re: NDsolve problem
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 3 Jul 2010 08:20:08 -0400 (EDT)

```With PlotRange->All you are zoomed in and looking at numerical noise. Use PlotRange->{0,10^-4} to see that the result is essentially constant.

Bob Hanlon

---- "ntina.86 at libero.it" <ntina.86 at libero.it> wrote:

=============
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[]], {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[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[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[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. >>

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