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MathGroup Archive 1997

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Re: NDSolve problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg6528] Re: [mg6511] NDSolve problem
  • From: Allan Hayes <hay at haystack.demon.co.uk>
  • Date: Sun, 30 Mar 1997 22:24:07 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Zahir Bishnani <z.bishnani at damtp.cam.ac.uk>
[mg6511] NDSolve problem

>>>>>>>>>>>
I am trying to solve a scalar ODE numerically but since evaluating  
the derivative involves a FindRoot operation, I get error messages.

Example:

If the function that gives the derivative is

FFunc1[y_]:= theta /. FindRoot[Cos[y*theta]==0.0, {theta,2,5}];

Trying NDSolve as follows just spouts out errors

NDSolve[{y'[x]==FFunc1[y[x]], y[0]==1.}, {y}, {x,0,1}]

<<<<<<<<<<<<

Zahir
The problem arises from the way that you are using FindRoot.
Trace the evaluation of FFunc1 by using a variant that prints out  
the values of theta as it is evaluated.

FFunc1P[y_]:=
theta /. FindRoot[Print[theta];Cos[y*theta]==0.0, {theta,2,5}];

For example (leaving out the message)

FFunc1P[0.005]
2.
5.
2.
5.
60.6231
631.9
339.622
306.864
314.173
314.159
314.159

Try some more values for y.
The roots that you find are all over!

The graph

Plot[Cos[3 x], {x,-1,6}]

explains this.

Allan Hayes
hay at haystack.demon.co.uk
http://www.haystack.demon.co.uk





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