Volume 26 • Number 1 • 2003   • Parabolic-Elliptic Correspondence of a Three-Level Finite Difference Approximation to the Heat Equation Mohd Salleh Sahimi, Norma Alias, Noreliza Abu Mansor and Norhalena Mohd Nor Abstract. 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 proceduce employing a fractional splitting strategy applied alternately at each intermediate time step. Full text: PDF