- Thread starter
- #1

Code:

```
Nmax = 10;
Mmax = 10;
A = 4/Pi^2*Integrate[x*Sin[n*x]*Sin[m*y], {x, 0, Pi}, {y, 0, Pi}];
B = 4/Pi^2*Integrate[Sin[n*x]*Sin[m*y], {x, 0, Pi}, {y, 0, Pi}];
u[x_, y_, t_] =
Sum[Sin[n*x]*
Sin[m*y] (A*Cos[(n^2 + m^2)*t] +
B/(n^2 + m^2)*Sin[(n^2 + m^2)*t]), {n, 1, Nmax}, {m, 1, Max}];
```

Code:

```
Nmax = 20;
Mmax = 20;
\[Lambda] = Table[n^2 + m^2, {n, 1, Nmax}, {m, 1, Mmax}];
u[x_, y_, t_] =
4/Pi^2*Sum[
Sin[n*Pi/2]*Sin[m*Pi/2]/\[Lambda][[n, m]]*Sin[n*x]*Sin[m*y]*
Sin[t*\[Lambda][[n, m]]], {n, 1, Nmax}, {m, 1, Mmax}];
```