       Re: NDSolve with implicit function

• To: mathgroup at smc.vnet.net
• Subject: [mg65891] Re: [mg65876] NDSolve with implicit function
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Fri, 21 Apr 2006 01:33:28 -0400 (EDT)
• References: <200604200915.FAA05354@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```rondeau at uvic.ca wrote:
> I am trying to numerically solve a differential equation
> {x'[t]==f[x[t],y[t]], x=a} , where y[t] is the numerical solution to an
> implicit function g[x[t],y[t]]==0 (not a polynomial).
>
> In other words, given x[t], we should be able to numerically compute y[t]
> from the implicit function and it would enter numerically into the function
> f of NDSolve.
>
> Anyone with an idea on how to do this?
>
> Thanks.
> Daniel

It looks like you are trying to solve a DAE equation. Here is an example:

f[a_,b_]:=Cos[a b]
g[a_,b_]:=Erf[a]+Sin[b]+a b

NDSolve[{x'[t]==f[x[t],y[t]],g[x[t],y[t]]==0,x==1},{x,y},{t,0,1}]

In:=
NDSolve[{Derivative[x][t] == f[x[t], y[t]], g[x[t], y[t]] == 0, x
== 1}, {x, y}, {t, 0, 1}]

Out=
{{x -> InterpolatingFunction[{{0., 1.}}, <>], y ->
InterpolatingFunction[{{0., 1.}}, <>]}}

Carl Woll
Wolfram Research

```

• Prev by Date: Re: NDSolve with implicit function
• Next by Date: Re: command line question
• Previous by thread: NDSolve with implicit function
• Next by thread: Re: NDSolve with implicit function