Geodesic
Implicit for local effects and explicit for nonlocal effects is unconditionally stable
Electronic transactions on numerical analysis, Tome 18 (2004), pp. 174-187.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit in local and stabilizing terms in the underlying PDE and explicit in nonlocal and unstabilizing terms. Unconditional stability and convergence of the numerical scheme are proved by the energy method and by algebraic techniques. This stability result is surprising because usually when different methods are combined, the stability properties of the least stable method plays a determining role in the combination.
Classification : 76D05, 35Q30, 90C31
Keywords: unconditional stability, implicit-explicit methods, multiscale integration 
@article{ETNA_2004__18__a2,
     author = {Anitescu, Mihai and Pahlevani, Faranak and Layton, William J.},
     title = {Implicit for local effects and explicit for nonlocal effects is unconditionally stable},
     journal = {Electronic transactions on numerical analysis},
     pages = {174--187},
     publisher = {mathdoc},
     volume = {18},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__18__a2/}
}
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%A Layton, William J.
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Anitescu, Mihai; Pahlevani, Faranak; Layton, William J. Implicit for local effects and explicit for nonlocal effects is unconditionally stable. Electronic transactions on numerical analysis, Tome 18 (2004), pp. 174-187. http://geodesic.mathdoc.fr/item/ETNA_2004__18__a2/