Optimal second order diagonally implicit SSP Runge--Kutta methods

2014/09/30 by Tihamér A. Kocsis, Kocsis, Tihamér A., Adrián Németh +1
Engineering · Mathematics · #65L06 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #G.1.7 #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1409.8583

openalex publication_date 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Optimal Strong Stability Preserving (SSP) Runge--Kutta methods has been widely investegated in the last decade and many open conjectures have been formulated. The iterated implicit midpoint rule has been observed numerically optimal in large classes of second order methods, and was proven to be optimal for some small cases, but no general proof was known so far to show its optimality. In this paper we show a new approach to analytically investigate this problem and determine the unique optimal methods in the class of second order diagonally implicit Runge--Kutta methods.

Citations

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

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