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 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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. 
@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/}
}
TY  - JOUR
AU  - Mohd Salleh Sahimi
AU  - Norma Alias
AU  - Noreliza Abu Mansor
AU  - Norhalena Mohd Nor
TI  - Parabolic-Elliptic Correspondence
                        of a Three-Level Finite Difference Approximation to the
                        Heat Equation
JO  - Bulletin of the Malaysian Mathematical Society
PY  - 2003
VL  - 26
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BMMS_2003_26_1_a9/
ID  - BMMS_2003_26_1_a9
ER  - 
%0 Journal Article
%A Mohd Salleh Sahimi
%A Norma Alias
%A Noreliza Abu Mansor
%A Norhalena Mohd Nor
%T Parabolic-Elliptic Correspondence
                        of a Three-Level Finite Difference Approximation to the
                        Heat Equation
%J Bulletin of the Malaysian Mathematical Society
%D 2003
%V 26
%N 1
%U http://geodesic.mathdoc.fr/item/BMMS_2003_26_1_a9/
%F BMMS_2003_26_1_a9
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/