Any of a class of partial differential equations describing phenomena that do not change from moment to moment, as when a flow of heat or fluid takes place within a medium with no accumulations. The Laplace equation, uxx + uyy = 0, is the simplest such equation describing this condition in two dimensions. For the following four problems, I have used FDM to discretize Laplace's equation and then the equation was solved numerically using two different iterative methods entitled "Line by Line Iterative Method" and "The Five-Point Method" in order to find the distribution of temperature in a solid body or flow of fluid.

1. Potential Flow Over a Backward-Facing Step

2. 2D Steady-state Heat Conduction on a Plate with Dirichlet Conditions

3. 2D Steady-state Heat Transfer Problem with Convection, and Conduction Boundary Conditions

4.  Heating a Plate via Convection Mechanism on Boundaries