At moment t I have:
x(t) = w(t) / h^2
e(t) = 10w(t) + 6.25h - 5g + 5
f(t) = a*(x(t))^2 + b*(x(t)) + c
And at moment t+1 I have:
x(t+1) = x(t) - [e(t) * f(t)] / (k*h^2)
a, b, c, g, h and k are constants. t is time starting at 0.
I need to find how much time does it take to change, for example, x=200 to x=100.
I have been trying to create a generic function x(t) and integrate it.
But I am having problems with it ...
Update
To better clarify the algorithm given a x(t) to obtain x(t+1) I do: 1 - Calculate current energy level, e(t), using x(t); 2 - Calculate factor e(t) using x(t); 3 - Calculate x(t+1) using x(t), e(t) e f(t)
This said x(t+1) as a function of only x(t) = x and constants is:
x(t+1) = [-10ah*x^3 - (6.25a+10bh)*x^2 -(6.25b+10ch+hk)*x - 6.25chk] / (hk)
So it is a third degree polynomial ...
But how to find how much time does it take decrease x from 200 to 100?
How to plot such a function? I mean, can I define x(t) as not recursive?