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MathGroup Archive 1999

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Re: How to NDSolve the differential equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19640] Re: How to NDSolve the differential equation
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 7 Sep 1999 00:28:36 -0400
  • Organization: Universitaet Leipzig
  • References: <7qulo3$2r5@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Chee,

your equation is singular at the origin. How ever a convergent power
series 
exist and a numerical solution is possible.

The problem ov NDSolve[] ist that it divedes the equation by x and get
Sin[x]/x but it does not calculate a Limit[] at x->0 it just find a
(not existing) singulaity. You cando the following:
Define the Sin[x]/x function


deqn = x y''[x] + Sin[x] y'[x] + 2 x y[x] == 0

sinc[0.] := 1
sinc[0] := 1
sinc[x_?NumericQ] := Sin[x]/x

deqn2 = (Simplify[#/x & /@ deqn]) /. Sin[x]/x -> sinc[x]

and 

NDSolve[{deqn2, y[0] == 0, y'[0] == 1}, y[x], {x, 0, 2}]

works as expected.

Hope that helps
  Jens


Chee Lim Cheung wrote:
> 
> Dear Mathematica gurus & users,
> 
> I encountered error messages with the tag Power::infy when I tried to do
> the following:
> 
> NDSolve[{x y''[x] + Sin[x] y'[x] + 2 x y[x] == 0,y[0]==0, y'[0]==1}, y,
> {x,0,2}]
> 
> Can anyone help me in getting Mathematica to produce an answer? I am using
> Mathematica 4.0 & Mathematica 3.0.
> 
> Thanks
> Chee


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