Strong Stability-Preserving High-Order Time Discretization Methods

. In this paper wer#1A43 andfur#41; develop a class ofstr#1X stability-pr#it.7A3A (SSP) high-or#/3 time discr#:44.2XFFX for semidiscr#2X method of lines appr# ximations ofpar# tialdi#er#4 tial equations.Pr#;31.r#X ter#at TVD (total var#X1F1. diminishing) time discr#3:/.2XX;31 thesehigh-or#A3 timediscr#/A3.2X7; methodspr#77A: e thestr#7: stabilitypr #1 er#1/; offir#A3;;.2X Euler time stepping and havepr# ved ver# useful, especially in solving hyper# olicpar#.1: di#er#: tial equations.The new developments in this paper include theconstr#X.2X3 of optimal explicit SSPlinear Runge--Kutta methods,their application to thestr#1F stability of coer#74 eappr# ximations, a systematic study of explicit SSP multistep methodsfor nonlinear pr#linear and the study of the SSP pr#. er# y of implicit Runge--Kutta and multistep methods. Key words.str#14 stabilitypr#1XX.27F/ Runge--Kutta methods, multistep methods, high-or#.2 accur #cu , timediscr#43;.27F3 AMS subjectclctj44k7kj3,N 65M20, 65L06 PII. S003614450036757X 1.