Geodesic
Parabolic-Elliptic Correspondence of a Three-Level Finite Difference Approximation to the Heat Equation
Bulletin of the Malaysian Mathematical Society, Tome 26 (2003) no. 1 
Mohd Salleh Sahimi; Norma Alias; Noreliza Abu Mansor; Norhalena Mohd Nor. Parabolic-Elliptic Correspondence
                        of a Three-Level Finite Difference Approximation to the
                        Heat Equation. Bulletin of the Malaysian Mathematical Society, Tome 26 (2003) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2003_26_1_a9/
@article{BMMS_2003_26_1_a9,
     author = {Mohd Salleh Sahimi and Norma Alias and Noreliza Abu Mansor and Norhalena Mohd Nor},
     title = {Parabolic-Elliptic {Correspondence
}                        of a {Three-Level} {Finite} {Difference} {Approximation} to the
                        {Heat} {Equation}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2003},
     volume = {26},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2003_26_1_a9/}
}
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                        of a Three-Level Finite Difference Approximation to the
                        Heat Equation
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Voir la notice de l'article provenant de la source BMMS

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.