NDSolve with side conditions:
- To: mathgroup at smc.vnet.net
- Subject: [mg32709] NDSolve with side conditions:
- From: steger at uni-greifswald.de (Thomas Steger)
- Date: Thu, 7 Feb 2002 05:09:37 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
The following ordinary differential equation system is given:
y'(t)=f1[y(t),x(t),z(t)]; x'(t)=f2[y(t),x(t),z(t)] and
z(t)=f3[y(t),x(t)]. z(t) is given in implicite and integrated form.
The question reads as follows: Can Mathematica solve this system
numerically by NDSolve. I have tried the following syntax:
NDSolve[{y'[t]==f1[y[t], x[t], z[t]], x'[t]==f2[y[t], x[t], z[t]],
z(t)==f3[y[t], x[t]], y[0]==y0, x[0]==x0, z[0]==z0},{y[t], x[t],
z[t]},{t, 0, 100}].
I could differentiate z(t)=f3[y(t),x(t)] with respect to t; this would
yield a standard 3-dimensional DES. But I would like not to increase
the dimension.
Thanks for any help!