Problem: Solve \(\nabla ^{2}T\left (x,y\right )=0\) on the following plate, with height \(h=30\), and width \(w=10\), and with its edges held at ﬁxed temperature as shown, ﬁnd the steady state temperature distribution

System boundary conditions.

Mathematica NDSolve[] does not currently support Laplace PDE as it is not an initial value problem.

Jacobi iterative method is used below to solve it. 100 iterations are made and then the resulting solution plotted in 3D.