# Solving the heat equation

Calculus 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.