```
(*simple example showing how to use Manipulate to animate the
solution of the Poisson 2D PDE using the Jacobi method.
Nasser M. Abbasi, March 6, 2012*)

Manipulate[

Module[{h, u, grid, force, f},
h = 1/(n - 1);
u = Table[0, {n}, {n}];
grid = makeCoordinates[n];
f[x_, y_] := -Exp[-(x - 0.25)^2 - (y -
0.6)^2]; (*the force function*)

force = Map[f[#[[1]], #[[2]]] &,
grid, {2}]; (*evaluate it on the grid*)

Do[ (*solve*)
jacobiStep[Unevaluated@u, h, force], {n}
];

(*plot the solution*)

ListPlot3D[u, PlotRange -> All, PerformanceGoal -> "Quality",
ImagePadding -> 30, ImageSize -> 400, Mesh -> {n, n},
PlotLabel ->
Text@Row[{"solution to ",
HoldForm[-Power["\[Del]", 2] "u"[x,
y] == -Exp[-(x - 0.25)^2 - (y - 0.6)^2]]]]}]
]
],

{{n, 9, "number of steps"}, 5, 31, 1, Appearance -> "Labeled"},
TrackedSymbols :> {n},
Initialization :>
{
jacobiStep[u_, h_, f_] := Module[{nRow, nCol, i, j},
{nRow, nCol} = Dimensions[u];
For[i = 2, i < nRow, i++,
For[j = 2, j < nCol, j++,
u[[i,
j]] = (1/4) (u[[i - 1, j]] + u[[i + 1, j]] + u[[i, j - 1]] +
u[[i, j + 1]] - h^2 f[[i, j]])
]
]
];

makeCoordinates[n_] := Module[{i, j, h},
h = 1/(n - 1);
N@Table[{i*h, j*h}, {i, 0, n - 1}, {j, 0, n - 1}]
];

}
]
```