       solving simple ODE using NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg6498] solving simple ODE using NDSolve
• From: Zahir Bishnani <z.bishnani at damtp.cam.ac.uk>
• Date: Thu, 27 Mar 1997 02:42:33 -0500 (EST)
• Organization: DAMTP, University of Cambridge, UK.
• Sender: owner-wri-mathgroup at wolfram.com

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

Example:

Given the derivative function

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

which is pretty much equivalent to

FFunc2[y_]:= N[ArcCos/y];

Trying NDSolve as follows just spouts out errors

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

FindRoot::precw: Warning: The precision of the argument function
(Cos[y[x] theta] - 0.) is less than WorkingPrecision (16).
FindRoot::frnum: Function {Cos[2. y[x]]} is not a length 1 list
of numbers at theta = 2..
ReplaceAll::reps: {FindRoot[Cos[y[x] theta] == 0., {theta, 2, 5}]}
is neither a list of replacement rules nor a valid dispatch
table, and so cannot be used for replacing.

Does anyone know how I could get around this problem?

Cheers,

Zahir

```

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