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How to get a simple system of recursion equations to give output?

Iuval Clejan

Posted 10 hours ago

This seems to not converge, no output after a day. Is there another way to do it, that will give output? It's just a system of recursion equations, with boundary conditions at 1 and N (here N=3).

POSTED BY: Iuval Clejan

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Bill Nelson

Posted 1 hour ago

This may or may not help you. If you try FullSimplify[Collect[Eliminate[{ x[1]==f11[x[2],y[2]], y[1]==f12[x[2],y[2]], x[2]==fx[x[1],y[1],x[3],y[3]], y[2]==fy[x[1],y[1],x[3],y[3]], x[3]==f31[x[2],y[2],0], y[3]==f32[x[2],y[2],0]}, {x[2],y[2],x[3],y[3]}], {x[1],y[1]}]] then it will quickly show you expr1x[1]+expr2y[1]==0 && expr3x[1]+expr4y[1]==0 && expr5x[1]+expr6y[1]==0 Each of those six new expressions are large, but this has removed x[2],y[2],x[3],y[3] and perhaps you can see something in those expressions that will tell you something about the solution you are looking for.

This may or may not help you. If you try

FullSimplify[Collect[Eliminate[{
    x[1]==f11[x[2],y[2]],
    y[1]==f12[x[2],y[2]],
    x[2]==fx[x[1],y[1],x[3],y[3]],
    y[2]==fy[x[1],y[1],x[3],y[3]],
    x[3]==f31[x[2],y[2],0],
    y[3]==f32[x[2],y[2],0]},
    {x[2],y[2],x[3],y[3]}],
  {x[1],y[1]}]]

then it will quickly show you

expr1*x[1]+expr2*y[1]==0 &&
expr3*x[1]+expr4*y[1]==0 &&
expr5*x[1]+expr6*y[1]==0

Each of those six new expressions are large, but this has removed x[2],y[2],x[3],y[3] and perhaps you can see something in those expressions that will tell you something about the solution you are looking for.

POSTED BY: Bill Nelson