Implicit Discrete Map with MatContM

[Yassine Karoui]

Hello,

I checked the four Tutorials and the documentation for MatContM and was wondering if I could use it to analyse my Discrete implicit Map.
All the examples treat explicit cases (the new state depends only on the old state x+ = f(x-) )
My map is a poincaré section, detecting impact events. The equations are nonlinear and implicit (x+ = f(x-,x+) )
for example :
c * (sin( x(n+1) ) - sin( x(n) ) + y(n) * (x(n+1) - x(n) ) - a = 0
c * (sin( x(n+2) ) - sin( x(n+1) ) + y(n+1) * (x(n+2) - x(n+1) ) + a = 0 ....
Is it possible to use MatContM in such case ?

Thanks !!

[hilmeijer]

This is possible, what you need is a function such that you have get the new value.

So if you have a nonlinear equation, you could use fsolve to get the root, or your Newton iteration. The system definition could involve any function, but then do not use Symbolic derivatives, but only numerical (finite differences). It's a bit of programming but certainly possible.

Hil

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From: Ahmed Yassine Karoui yassine-k@users.sourceforge.net
Sent: Saturday, April 18, 2020 11:34 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Implicit Discrete Map with MatContM

Hello,

I checked the four Tutorials and the documentation for MatContM and was wondering if I could use it to analyse my Discrete implicit Map.
All the examples treat explicit cases (the new state depends only on the old state x+ = f(x-) )
My map is a poincaré section, detecting impact events. The equations are nonlinear and implicit (x+ = f(x-,x+) )
for example :
c * (sin( x(n+1) ) - sin( x(n) ) + y(n) * (x(n+1) - x(n) ) - a = 0
c * (sin( x(n+2) ) - sin( x(n+1) ) + y(n+1) * (x(n+2) - x(n+1) ) + a = 0 ....
Is it possible to use MatContM in such case ?

Thanks !!

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Implicit Discrete Map with MatContM

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