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Straighforward iteration with mathematica instead of recursion.

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.

POSTED BY: Thomas Winkler
2 Replies

Okay, it looks like you are building a nested expression. It might be getting huge and that could account for the speed issue. Given the use of machine doubles, large scales, and high degree exponents, I would be surprised if this was not numerically very poorly behaved in any case.

POSTED BY: Daniel Lichtblau

Your (unbalanced) parenthesization makes this not parse. Which means it is difficult to determine what might be the issue(s).

POSTED BY: Daniel Lichtblau
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