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NDSolve with InverseFunction of a solution. (game theoretical)

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  • 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.


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