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[0]=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[0]==1},{x,y},{t,0,1}] In[14]:= NDSolve[{Derivative[1][x][t] == f[x[t], y[t]], g[x[t], y[t]] == 0, x[0] == 1}, {x, y}, {t, 0, 1}] Out[14]= {{x -> InterpolatingFunction[{{0., 1.}}, <>], y -> InterpolatingFunction[{{0., 1.}}, <>]}} Carl Woll Wolfram Research

**References**:**NDSolve with implicit function***From:*rondeau@uvic.ca