Hello,
I want to use a straightforward iteration method to calculate a function which depends on itself at the previous step. It was able to solve it as a recursion function for a small value of steps, but they are far from where I want to go and it takes a long time to solve it.
Maybe you can help me.
The code for the recursion function is given (here the most essential part) by:
f[L2_][t_] := 0 /; L2 < 0;
f[0][ t_] :=a*(Exp[-4 Log[2] (t/tt)^2]);
f[1][t_] := a*(f[0][t]] - b*(f[0][t])^k)*10^-9) ;
f[L2_][t_] :=
f[L2][t] = f[L2 - 1][ t] - b*(f[L2-1][t])^k)*10^-9);
a,b,k,tt are constants.
Already for values of L2>15 the calculation takes a long long time. So far away from what I want L2 > 1000.
So I would like to have just a simple iteration method:
Solving f
for a certain L2
use the solution to calculate another function and then put the solution of f[...,L2,...]
into the calculation of f[...,L2+1,...]
. And so on.. so that at the end I got a table of the values of f in dependency of L2..
But even using For-Loops it did not work.
So is there a way that Mathematica is able to solve this problem?
Thank you very much in advance!
Thomas
P.S.
b = 1.67575*10^-85; a = 1*10^18: tt=35*10^-15;
t goes from -100*10^-15 to 100*10^-15; k=6
Maybe it is also important to know that usualy I use the solution as an input function for a differential equation. Furtheremore f is usualy also dependent on the solution of the differential equation (from a step before). Thats why I want an iterative method.