What is eq
? I cannot reproduce the error
n = 4;
h = 2/n;
Table[u[0, j] = 0, {j, 1, n}];
Table[u[n, j] = j*h*(2 - j*h), {j, 1, n}];
Table[u[i, 0] = 0, {i, 1, n}];
Table[u[i, n] = i h, {i, 0, Floor[n/2]}];
Table[u[i, n] = 2 - i h, {i, Floor[n/2 + 1], n}];
eq = Table[
u[i + 1, j] + u[i - 1, j] + u[i, j + 1] + u[i, j - 1] - 4*u[i, j] ==
0, {i, 1, n - 1}, {j, 1, n - 1}]
eq1 = Flatten[eq]
var = Table[u[i, j], {i, 1, n - 1}, {j, 1, n - 1}];
Solve[eq1, Flatten@var]
eq1 = Flatten[eq]
var = Table[u[i, j], {i, 1, n - 1}, {j, 1, n - 1}];
var1 = Flatten[var];
Solve[eq1, var1]
Result is the same.