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I'm trying to solve a differential equation which solution is in the form of Bessel functions. One of the boundary conditions is at infinity. I use:

ψ[R_] = ψ[R] /. DSolve[{ψ''[R] + (ψ'[R])/R - κ^2 ψ[R] == 0,
                        ψ[a/2] == Psi0, ψ[M] == 0}, ψ[R], R][[1]]

Limit[ψ[R], M -> Infinity]

Simplify[%, {r > 0 && κ > 0 && a > 0 && Psi0 ∈ Reals}]

And obtain:

Problem

How can I obtain the solution of my problem overpassing the time limit?

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  • $\begingroup$ With Maple I have a simple answer: \[Psi][R] =(Psi0 BesselK[0, k R])/BesselK[0, (a k)/2] $\endgroup$
    – Mariusz Iwaniuk
    Jan 9, 2019 at 20:16
  • $\begingroup$ Could you print here your system info. I am getting a Recursion Limit error and not reproducing your resulted time limit error. $\endgroup$
    – Jose Enrique Calderon
    Jan 10, 2019 at 9:09

2 Answers 2

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Change the order of execution.

ψ[R_] = ψ[R] /. 
  DSolve[{ψ''[R] + (Derivative[1][ψ][R])/ R - κ^2 ψ[R] == 0, ψ[a/2] == Psi0, ψ[M] == 0}, ψ[R], R][[1]]

$Assumptions = 
 r > 0 && κ > 0 && a > 0 && Psi0 ∈ Reals && M > 0 && R > 0

ψ[R_] = FullSimplify[ψ[R]]  

(*(Psi0 (BesselI[0, M κ] BesselK[0, R κ] - BesselK[0, M κ] BesselI[0, R κ]))/( BesselK[0, (a κ)/2] BesselI[0, M κ] - 
 BesselI[0, (a κ)/2] BesselK[0, M κ])*)

Limit[ψ[R], M -> ∞]
(*(Psi0 BesselK[0, R κ])/BesselK[0, (a κ)/2]*)
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TimeConstraint helps to increase the time limit spent on Simplify operation. In case this is just a computation time issue and not an algorithmic one, this would help.

https://reference.wolfram.com/language/ref/TimeConstraint.html

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