numerical technics in engineering

Here is a typical steady-state heat 

ow problem. Consider a thin steel plate to be a

10  20 (cm)2 rectangle. If one side of the 10 cm edge is held at 1000C and the other

three edges are held at 00C, what are the steady-state temperature at interior points?

We can state the problem mathematically in this way if we assume that heat 

ows

only in the x and y directions:

Find u(x; y) (temperature) such that