Eigenvalue problem in mathematica...

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From: bulash on 21 Nov 2008 05:31

---

I have serious problem with an eigenvalue problem. I need symbolic solution and using ODE.m package. I wrote my notebook to mathematica but it crashes or never finish for 1 week!!!

The noebook is following, best wishes:

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From: sjoerd.c.devries on 25 Nov 2008 07:17

---

Bulash,

I can see several problems here:

First, what is this ODE package? As far as I know, differential
equations are done in Mathematica using DSolve or NDsolve. Are you
sure you're not using a another system's package or so (they end in .m as well)?
Anyways, I don't see a statement in your program in which you load
this package (Needs[ ] or <<), so don't expect Mathematica to know the
ODE function automatically.

And then there is the use of the set delayed construction ( := ) for
all of your assignments, even involving constants. For constants, :=
is never essential or useful and Set ( = ) usually yields a much
faster program.

The difference between the two is that in an assignment like a=b+5 the
right-hand side is evaluated immediately and the result is used
whenever the righthand side is used. The value of b at the time of the
assignment to a is used.

In a:=b+5 the right-hand side is *not* evaluated until a is actually
used in an evaluation. The value of b at that time is used, *not* the
value at the time of the assignment to a.

Your definition of p ("p[r_] := e^Integrate[B[r]/A[r], r]") has
several problems:

I assume you want e to be the exponential constant. That should be
either entered as E or esc-ee-esc in Mathematica.

The integral itself is a very complicated function and will take for
ages to solve (if a solution can be found at all, of which I'm not
sure). Due to the ':=' it is calculated *every* time p[r] is used.

Furthermore, if you would like to evaluate p[5] this would yield
e^Integrate[B[5]/A[5], 5] which is clearly nonsense (no integration
variable left here). You should really use '=' here. Or perhaps you
meant something like: p[r_] := E^Integrate[B[r1]/A[r1], {r1,0,r}] ?

Cheers -- Sjoerd

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