Background
The alternating direction implicit (ADI) method is a finite difference method for solving differential equations. It is most notably used to solve the problem of heat conduction or solving the diffusion equation in 2 or more dimensions.
The traditional method for solving the heat conduction equation is the method of Crank-Nicolson. This method is implicit, but has an unaffordable stability criterion in 2 or more dimensions.
Example
Consider the linear diffusion equation in two dimensions, Failed to parse (unknown function "\del"): {\displaystyle \frac{\partial u}{\partial t} = \del^2 u}