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!