       Re: solving differential equations

• To: mathgroup at smc.vnet.net
• Subject: [mg3517] Re: [mg3484] solving differential equations
• From: jpk at apex.mpe.FTA-Berlin.de (Jens-Peer Kuska)
• Date: Wed, 20 Mar 1996 02:49:35 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```> Mathgroup,
>
> I have a system of ODE I wish to solve numerically of the form X'[t] =
> F(X[t])/|F(X[t])| for a given function
>         F : plane -> plane
> and given intial conditions. NDSolve works well on this except where the
> system is ill-behaved, in particular, where F = 0. I can replace this
> system with another one that has equivalent solutions and is usually
> well-behaved where F = 0. However, I don't want to make the replacement
> unless I have to, and only near where F = 0. (I wish to construct a command
> that gives the solution for an inputted function F.)
>
> Is there any way possible to do this with NDSolve? In other words, as it
> steps along have it check the value of F. If its magnitude ever gets too
> close to 0, have it use the other system.

> Thanks,
> Steve Wilkinson
>
>
Hi Steve,

here is the solution for F[x]=Sin[x]

sol=
NDSolve[
{y==0,
y'[t]== If[ z=Sin[t]; Abs[z]>\$MachineEpsilon,
(* then *)
z/Abs[z],
(*else *)
1
]},
y[t],{t,0,4Pi}
];

{{y[t] ->

InterpolatingFunction[{0.,

12.5664}, <>][t]}}

Plot[Evaluate[
y[t] /. Flatten[sol]],{t,0,4Pi}]

Hope that helps
Jens

==== [MESSAGE SEPARATOR] ====

```

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