Suppose I have to solve the 2-D heat equation in a rectangular domain using the finite difference method, for the boundary conditions say:
$T_1$ is the temperature of the right side of the rectangle,
$T_2$ is the temperature of the top side,
$T_3$ is the temperature of the left side, and $T_4$ is the temperature at the bottom.
T2 _______________ | | T3 | |T1 | | |_______________| T4
at the vertices points of the rectangle, how to set the boundary conditions? do I need to take the average value of the two temperatures?