# Recurrence table doesn't like non-linearity?

When I evaluate the following RecurrenceTable expression

RecurrenceTable[
{x[n + 1] == x[n] + 0.1 y[n],
y[n + 1] == y[n] + 0.1 z[n],
z[n] == x[n] + 1,
x[1] == 2., y[1] == 3.},
{x, y, z}, {n, 1, 10}]


it does what I expect. However, if I change the x[n] + 1 into x[n]^2, it no longer works, despite the fact that there is no circularity in the table. I don't see why it would make a difference what z is as a function of x.

What's the reason for this behavior? Is it documented?

• The Scope - Difference-Algebraic Equations section of the reference page for RecurrenceTable gives an example of "a linear difference-algebraic equation with constant coefficients". Maybe a nonlinear one is outside the scope? In your example, you could define z[n_] := x[n]^2 outside the RecurrenceTable I think. Mar 25 '18 at 1:02

Eliminating the decimal points fixes the problem

N[RecurrenceTable[
{x[n + 1] == x[n] + 1/10 y[n],
y[n + 1] == y[n] + 1/10z[n],
z[n] == x[n]^2,
x[1] == 2, y[1] == 3}, {x, y, z}, {n, 1, 10}]]


gives

{{2.,3.,4.},{2.3,3.4,5.29},{2.64,3.929,6.9696},{3.0329,4.62596,9.19848},
{3.4955,5.54581,12.2185},{4.05008,6.76766,16.4031},{4.72684,8.40797,22.343},
{5.56764,10.6423,30.9986},{6.63187,13.7421,43.9817},
{8.00608,18.1403,64.0973}}


Perhaps it is a pattern matching problem fighting inexact decimals