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Strong Stability-Preserving High-Order Time Discretization Methods
Abstract
In this paper we review and further develop a class of strong stability-preserving (SSP) high-order time discretizations for semidiscrete method of lines approximations of partial differential equations. Previously termed TVD (total variation diminishing) time discretizations, these high-order time discretization methods preserve the strong stability properties of first-order Euler time stepping and have proved very useful, especially in solving hyperbolic partial differential equations. The new developments in this paper include the construction of optimal explicit SSP linear Runge--Kutta methods, their application to the strong stability of coercive approximations, a systematic study of explicit SSP multistep methods for nonlinear problems, and the study of the SSP property of implicit Runge--Kutta and multistep methods.
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Citations
Cited by
High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
Shu, C.-W. (2009) · SIAM Review · doi:10.1137/070679065 · Cited by 964
Self-citationGriffith, B. E., & Peskin, C. S. (2005) · Journal of Computational Physics · doi:10.1016/j.jcp.2005.02.011 · Cited by 299
Finite-volume schemes for shallow-water equations
Kurganov, A. (2018) · Acta Numerica · doi:10.1017/s0962492918000028 · Cited by 108
Metadata
- Authors
- Gottlieb, S., Shu, C.-W., & Tadmor, E.
- Venue
- SIAM Review
- Published
- 2001-01
- Volume
- 43
- Issue
- 1
- Pages
- 89-112
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2116729868
- Cited by
- 2,565
- References
- 0
- FWCI
- 29.62
- Type
- journal article
- Language
- en
- Open access
- closed
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- Gottlieb, S., Shu, C.-W., & Tadmor, E. (2001). Strong Stability-Preserving High-Order Time Discretization Methods. SIAM Review. https://doi.org/10.1137/s003614450036757x
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