NDSolve with InverseFunction of a solution. (game theoretical)
- To: mathgroup at smc.vnet.net
- Subject: [mg45164] NDSolve with InverseFunction of a solution. (game theoretical)
- From: ktakeuch at umich.edu (Kan Takeuchi)
- Date: Fri, 19 Dec 2003 06:57:30 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hello,
I am trying to numerically solve a 2-dimentional (x,t) ODE system.
The general solution is like, for all x in (0,1),
D[ f[x,t] , t ] == g1[ x, u[x,t] , Integrate[ f[y,t] , {y,A,B} ] , t ],
D[ u[x,t] , t ] == g2[ x, u, t ],
where g's are functions, for which I have already got their
explicit expressions. But let me omit, as they are so complicated.
The problem would be that A and B are the values of
InverseFunction of f, namely,
A = min{ y such that f(y) = x } and B = max{ y such that f(y) = x }.
Can anyone tell me if NDSolve can handle, in principle,
inverse functions like this?
If so, would you tell me how I could do that, please?
Thank you very much for looking at.
Kan Takeuchi
Ph.D. candidate in Economics at the University of Michigan.