Download or read book Strong Stability Preserving High-order Time Discretization Methods written by Sigal Gottlieb and published by . This book was released on 2000 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we review and further develop a class of strong-stability preserving (SSP) high-order time discretizations for semi-discrete method-of-lines approximations of partial differential equations. Termed TVD (total variation diminishing) time discretizations before this class of high-order time discretization methods preserves the strong-stability properties of first-order Euler time stepping and has proved very useful especially in solving hyperbolic partial differential equations. The new contributions in this paper include the development of optimal explicit SSP linear Runge-Kutta methods, their application to the strong stability of coercive approximations, a systematic study of explicit SSP multi-step methods, and a study of the strong-stability preserving property of implicit Runge-Kutta and multi-step methods.