Solving the heat equationCalculus Level 4
A two-dimensional non-transient rectangular system follows the heat equation \[ \nabla^2 T = 0 \] where \(T(y,x)\) is the temperature at \((y,x)\).
- The system is 5 units wide (vertical) and 10 units (horizontal).
- The temperatures of north, east, west and south walls are maintained at 100, 40, 80 and 20 respectively.
What is the temperature of a point located 4 units to the right of the west wall and 2 units to the bottom of the north wall?
Note: This problem might require a numerical approach.