reccurent sequence

[rosenm]

Hello colleagues!
I would like to know:
1)how to solve reccurent sequences in Vensim PLE, for example: x(t+1)=x(t)+1;
2) how to solve system of nonlinear algebraic equations -for example x^2+y^25, x^2-y^2=1;
Thanks in advance

[tomfid]

1) A recurrent sequence that looks like a discrete-time dynamic model, like your example, is easy to solve:

x = INTEG( dx, x0 )
dx = ( (x+1) - x )/TIME STEP

Here dx represents the change from x(t) to x(t+1). Just be sure to use Euler or Diff integration.

2) This is possible using FIND ZERO in advanced versions of Vensim, but it's not really the purpose of the software. You could probably build a model that solves by representing iterations of Newton's method as time steps, but you'd be better off using some other package.

Tom

[rosenm]

Thanks for the answer;
About the nonlinear system - i am wondering , is there a method like realized in the attached file (for linear system 4x+2y=14; 2x+5y=-5), but applicable to nonlinear systems.


[Edited on 11-29-2010 by rosenm]

[tomfid]

Try http://en.wikipedia.org/wiki/Newton%27s_method

Tom

[rosenm]

Ok, Thank you very much Tom

[tomfid]

Hope it helps. Another place to look is the Numerical Recipes book series - I think there are some sections on nonlinear root finding.

Tom