Geodesic
Conditional stability of Larkin methods with non-uniform grids
Theoretical and applied mechanics, Tome 37 (2010) no. 2, p. 139 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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A stability analysis based on the von Neumann method shows that the Larkin methods for two-dimensional heat conduction using non-uniform grids are conditionally stable, while they are known to be unconditionally stable using uniform grids. The stability criteria consisting of the dimensionless time step Δt, the space intervals Δx, Δy, and the ratios of neighboring space intervals α, β are derived from the stability analysis. A subsequent numerical experiment demonstrates that solutions derived by the Larkin methods using non-uniform grids lose stability and accuracy when the criteria are not satisfied.
DOI : 10.2298/TAM1002139F
Classification : 80M20 80M25
Keywords: finite difference method, stability, heat conduction, Saul’yev method, Larkin method 
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     author = {Kazuhiro Fukuyo},
     title = {Conditional stability of {Larkin} methods with non-uniform grids},
     journal = {Theoretical and applied mechanics},
     pages = {139 },
     year = {2010},
     volume = {37},
     number = {2},
     doi = {10.2298/TAM1002139F},
     zbl = {1265.80009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/TAM1002139F/}
}
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Kazuhiro Fukuyo. Conditional stability of Larkin methods with non-uniform grids. Theoretical and applied mechanics, Tome 37 (2010) no. 2, p. 139 . doi: 10.2298/TAM1002139F

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