Geodesic
Implicit for local effects and explicit for nonlocal effects is unconditionally stable
Electronic transactions on numerical analysis, Tome 18 (2004), pp. 174-187
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},
     year = {2004},
     volume = {18},
     zbl = {1085.76046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__18__a2/}
}
TY  - JOUR
AU  - Anitescu,  Mihai
AU  - Pahlevani,  Faranak
AU  - Layton,  William J.
TI  - Implicit for local effects and explicit for nonlocal effects is unconditionally stable
JO  - Electronic transactions on numerical analysis
PY  - 2004
SP  - 174
EP  - 187
VL  - 18
UR  - http://geodesic.mathdoc.fr/item/ETNA_2004__18__a2/
LA  - en
ID  - ETNA_2004__18__a2
ER  - 
%0 Journal Article
%A Anitescu,  Mihai
%A Pahlevani,  Faranak
%A Layton,  William J.
%T Implicit for local effects and explicit for nonlocal effects is unconditionally stable
%J Electronic transactions on numerical analysis
%D 2004
%P 174-187
%V 18
%U http://geodesic.mathdoc.fr/item/ETNA_2004__18__a2/
%G en
%F ETNA_2004__18__a2
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/