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Re: I have an operator, How do I DSolve it?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96202] Re: I have an operator, How do I DSolve it?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Mon, 9 Feb 2009 05:34:34 -0500 (EST)
  • References: <gmndhs$s04$1@smc.vnet.net>

Hi,

I'm not sure to understand your question, because

B[m_, f_] := (D[f[#], {#, 2}] +
     1/# D[f[#], {#, 1}] + (1 - m^2/#^2) f[#]) &

does already what you want. If you don't like to have
the Function[{r},__] and prefer a Slot[] argument

G[m_, f_] :=
  Block[{r},
   DSolve[B[m, f][r] == 0, f, r][[1]] /.
    Function[{r}, expr_] :> Function @@ {expr /. r -> Slot[1]}]

Regards
   Jens

Aaron Fude wrote:
> Hi,
> 
> I have defined a differential operator, but what's the syntax for
> using it in DSolve?
> 
> I have the Bessel operator
> 
> B[m_, f_] := (D[f[#], {#, 2}] +
>     1/# D[f[#], {#, 1}] + (1 - m^2/#^2) f[#]) &
> 
> It's the Bessel operator for now, but I will soon replace it with a
> different one. This is for testing puposes only.
> 
> Now, how do I use it in DSolve?
> 
> So far I use
> 
> DSolve[S''[r] + 1/r S'[r] + (1 - m^2/r^2) S[r] == 0, S[r], r]
> 
> but that's not a good solution because I have to different expressions
> for the same thing. I want to used B only.
> 
> Many thanks in advance,
> 
> Aaron
> 


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