Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation - Sahimi, M. S.; Alias, N.; Mansor, N. A.; Nor, N. M. (2003)
We consider three-level difference replacements of parabolic equations focussing on the heat equation in two- space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an ADI method. Using the well-known fact of the parabolic-elliptic correspondence, we shall derive a two-stage iterative procedure employing a fractional splitting strategy applied alternately at each intermediate time step.