Implicit for local effects and explicit for nonlocal effects is unconditionallly stable.
Journal Article
·
· Electron. Trans. Numer. Anal.
OSTI ID:961457
A combination of implicit and explicit timestepping is analyzed for a system of ordinary differential equations (ODEs) motivated by ones arising from spatial discretizations of evolutionary partial differential equations (PDEs). 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.
- Research Organization:
- Argonne National Laboratory (ANL)
- Sponsoring Organization:
- SC; NSF
- DOE Contract Number:
- AC02-06CH11357
- OSTI ID:
- 961457
- Report Number(s):
- ANL/MCS/JA-47976
- Journal Information:
- Electron. Trans. Numer. Anal., Journal Name: Electron. Trans. Numer. Anal. Journal Issue: 2004 Vol. 18; ISSN 1068-9613
- Country of Publication:
- United States
- Language:
- ENGLISH
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