High order time discretization methods with the strong stability property
High order time discretization methods with the strong stability property
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Date
2001
Authors
Gottlieb, Sigal
Shu, Chi-Wang
Tadmor, Eitan
Advisor
Citation
S. Gottlieb, C.-W. Shu & E. Tadmor (2001). High order time discretization methods with the strong stability property. SIAM Review 43 (2001) 89-112.
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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.