Date: Mar 5, 2013 10:13 PM
Author: Iván Lazaro
Subject: Alternative to Table

Dear group:

I'm trying to build a code that evolves a grid of dimension 2gridDim+1
over a time timeDim. I managed to build such a code using Table with
only one problem: when the value of timeDim is of thousands, the time
it takes to evaluate is absurd. I tried to find an alternative way to
write this code, using NestList withouth success. NestList is able to
have an interator if I write it like #[[1]]+1, but it doesn't work
when I use it as an element of a list.

I let here a toy working example. Any input would be most appreciated.

Iv=E1n.


gridDim = 2; timeDim = 3;
list = ConstantArray[0, {2, 2*gridDim + 1, timeDim}];

Table[list[[1, i, 1]] = Sin[-(gridDim + 1.) + i], {i, 1,
2*gridDim + 1}];
Table[list[[2, i, 1]] = RandomReal[{0, 2*Pi}], {i, 1, 2*gridDim + 1}];


zUpdate[list_, t_] := Module[{lista},
lista = {};
lista = list;
Table[If[i + 1 > 2*gridDim + 1,
lista[[1, i, t + 1]] = list[[1, i, t]] (list[[2, 1, t]] -
list[[2, i - 1, t]]), If[
i - 1 == 0,
lista[[1, i, t + 1]] = list[[1, i, t]] (list[[2, i + 1, t]] -
list[[2, 2*gridDim + 1, t]]),
lista[[1, i, t + 1]] = list[[1, i, t]] (list[[2, i + 1, t]] -
list[[2, i - 1, t]])]],
{i, 1, 2*gridDim + 1}];
lista
];

pUpdate[list_, t_] := Module[{lista},
lista = {};
lista = list;
Table[If[i + 1 > 2*gridDim + 1,
lista[[2, i, t + 1]] = Mod[list[[1, i, t + 1]] (list[[2, 1, t]] -
list[[2, i - 1, t]]), 2*Pi],
If[i - 1 == 0,
lista[[2, i, t + 1]] = Mod[list[[1, i, t + 1]] (list[[2, i + 1,
t]] - list[[2, 2*gridDim + 1, t]]), 2*Pi],
lista[[2, i, t + 1]] = Mod[ list[[1, i, t + 1]] (list[[2, i + 1,
t]] - list[[2, i - 1, t]]), 2*Pi]]], {i, 1, 2*gridDim + 1}];
lista
];


Do[
list = zUpdate[list, i];
list = pUpdate[list, i];, {i, 1, timeDim - 1}];
list