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Strong stability-preserving high-order time discretization methods. (English) Zbl 0967.65098
This paper is essentially a review of a class of strong stability preserving (a.k.a. total variation diminishing) high-order time discretization methods for a broad class of partial differential equations. Emphasis is placed on nonlinear problems and problems with solutions of relatively low regularity, such as nonlinear conservation laws.

MSC:
65M12Stability and convergence of numerical methods (IVP of PDE)
65M20Method of lines (IVP of PDE)
65-02Research monographs (numerical analysis)
65L06Multistep, Runge-Kutta, and extrapolation methods
35L65Conservation laws