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MathGroup Archive 1998

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Re: NDSolve vs. DSolve


  • To: mathgroup@smc.vnet.net
  • Subject: [mg10931] Re: NDSolve vs. DSolve
  • From: Paul Abbott <paul@physics.uwa.edu.au>
  • Date: Thu, 12 Feb 1998 20:16:14 -0500
  • Organization: University of Western Australia
  • References: <6brh2k$ee9@smc.vnet.net>

Students wrote:

> In the following examples the DSolve solves easily while the NDSolve is
> producing the listed error messages. Why is that and how is it bypassed.
> 
> DSolve[y'''[x]==-Cos[x],y[0]==0,y[5]==0,y'[0]==0,y[x],x]
> 
> NDSolve[y'''[x]==-Cos[x],y[0]==0,y[5]==0,y'[0]==0,y[x],{x,0,5}]
> 
> NDSolve::unsol:
> Not possible to initiate boundary value problem with the chasing method

DSolve solves the differential equations and then fits the undetermined
coefficients using the boundary conditions.

For problems of this type you can use the shooting method (replacing
y[5]==0 with y''[0]==a and determining a):

In[1]:= system[a_]:= s= 

NDSolve[{y'''[x]==-Cos[x],y[0]==0,y'[0]==0,y''[0]==a},y,{x,0,5}]]//First

In[2]:= gun := y[5] /. system[#1] & 

In[3]:= FindRoot[gun[a] == 0, {a, 0, 0.3}] Out[3]= {a -> 0.476715}

In[4]:= y[5] /. s
Out[4]=
		          -12
		9.47337 10

In[5]:= Plot[Evaluate[y[x] /. s], {x, 0, 5}]

Cheers,
	Paul 

____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907       
mailto:paul@physics.uwa.edu.au  AUSTRALIA                            
http://www.pd.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________



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