Re: NDSolve with side conditions:
- To: mathgroup at smc.vnet.net
- Subject: [mg32751] Re: NDSolve with side conditions:
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 8 Feb 2002 03:49:24 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <a3tkmi$7e9$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi, Mathematicas build-in NDSolve command can't solve an algebraic differential equation. Since numerical solvers for algebraic differential equations are an active area of research you should look into the literature/netlib library to find a suitable algorithm. Regards Jens Thomas Steger wrote: > > 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!