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MathGroup Archive 2000

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Re: Question: numerical solution of nonlinear differential equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26413] Re: Question: numerical solution of nonlinear differential equation
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 20 Dec 2000 00:21:36 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <91f7n8$556@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

a) the equatio should be written with y'[x] and *not* with
   y[x]'  !

b)

In[]:=deqn = A y''[x] - B y'[x] + C Exp[-D*x] == 0;
      sol = y[x] /. First[DSolve[deqn, y[x], x]];
In[]:=sol /. Solve[{sol == 0 /. x -> 0, sol == 0 /. x -> E}, {C[1], 
        C[2]}] // FullSimplify

Out[]={(C*(E^(D*E) - E^((B/A + D)*E) - E^(D*x) + E^((B/A + D)*x) + 
    E^(D*(E + x))*(E^((B*E)/A) - E^((B*x)/A))))/
  (D*(B + A*D)*E^(D*(E + x))*(-1 + E^((B*E)/A)))}

c) NDSolve[] can't solve nonlinear boundary value problems,
   I don't know what you saw.

Regards
  Jens

Ronald Sastrawan wrote:
> 
> Hello !
> 
> I encountered a problem, trying to numerically solve a differential
> equation.
> My equation looks like:
> 
> A y''[x] - B y[x]' + C Exp[-Dx] == 0
> with boundary conditions: y'[0]==0 , y'[E]==0
> 
> All constants A to E are known.
> 
> Mathematica complains, that the equation is not linear. But in the
> online documentation I saw many examples of nonlinear differential
> equations, which all work fine. What is the difference between the
> examples and my equation ? And is there a possibility to NDSolve my
> equation ?
> 
> Any hint on this would be of great help to me.
> 
> Thanks a lot,
> 
> Ronald
> --


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