Numerical investigation of the parabolic mixed derivative diffusion equation via Alternating Direction Implicit methods

The two-dimensional analogue of a two-parameter mixed derivative equation is considered via two numerical methods: the ADI and compact ADI method. These methods are compared and the influence of the kinematic viscosity and viscoelasticity is discussed in relation to the solutions obtained. The two schemes are proven to be conditionally stable and the methods compared via an error analysis.