Strong Stability-Preserving High-Order Time Discretization Methods

On High Order Strong Stability Preserving Runge-Kutta and Multi Step Time Discretizations

Strong stability preserving (SSP) high order time discretizations were developed for solution of semi-discrete method of lines approximations of hyperbolic partial differential equations. These high order time discretization methods preserve the strong stability properties–in any norm or seminorm—of the spatial discretization coupled with first order Euler time stepping. This paper describes th...

High Order Strong Stability Preserving Time Discretizations

Strong stability preserving (SSP) high order time discretizations were developed to ensure nonlinear stability properties necessary in the numerical solution of hyperbolic partial differential equations with discontinuous solutions. SSP methods preserve the strong stability properties – in any norm, seminorm or convex functional – of the spatial discretization coupled with first order Euler tim...

A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods

A Survey of Strong Stability Preserving High Order Time Discretizations

Numerical solution for ordinary di erential equations (ODEs) is an established research area. There are many well established methods, such as Runge-Kutta methods and multi-step methods, for such purposes. There are also many excellent books on this subject, for example [1], [13] and [17]. Special purpose ODE solvers, such as those for sti ODEs, are also well studied. See, e.g., [6]. However, t...

Strong Stability Preserving Properties of Runge-Kutta Time Discretization Methods for Linear Constant Coefficient Operators

Strong stability preserving (SSP) high order Runge–Kutta time discretizations were developed for use with semi-discrete method of lines approximations of hyperbolic partial differential equations, and have proven useful in many other applications. These high order time discretization methods preserve the strong stability properties of first order explicit Euler time stepping. In this paper we a...