Strong Stability Preserving Methods


Optimized Methods For nonlinear nonautonomous systems: Explicit methods Runge-Kutta Multistep Multistep Multistage (MSRK) Implicit methods Runge-Kutta Multistep For linear, autonomous systems: Explicit methods Runge-Kutta Multistep Implicit methods Runge-Kutta Multistep Matlab Scripts Paper Scripts Test Suite Bibliography	Strong stability preserving methods (also known as total variation diminishing, contractivity preserving, or monotonicity preserving methods), are numerical methods for solving ordinary differential equations. They were developed for the time integration of semi-discretizations of hyperbolic conservation laws. The exact solutions of scalar conservation laws have the property that their total variation does not increase in time. Semi-discretizations are often designed so that their discrete solutions also have this property under forward Euler integration. SSP methods are higher order methods that also preserve this property. Because of this, they were originally referred to as TVD methods. However, they have the stronger property that they will preserve any convex functional bound (such as, e.g., positivity) that is satisfied under forward Euler integration. This page is a repository for information on SSP methods, including coefficients of optimal methods. This website was developed by David Ketcheson, Daniel Higgs, and Sigal Gottlieb and is currently maintained by Daniel Higgs. The development of the methods in this web site and the numerical test suite were partially supported by funding from AFOSR grant numbers FA-9550-09-1-0208 and FA-9550-12-1-0224 and by KAUST grant number FIC/2010/05.

Saturday, 21-Dec-2024 05:33:51 MST