LIRK-W: Linearly-implicit Runge-Kutta methods with approximate matrix factorization

2016/11/21 by Paul Tranquilli, Tranquilli, Paul, Adrian Sandu +3
Computer Science · Engineering · Mathematics · #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1611.07013

openalex publication_date 2016/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper develops a new class of linearly implicit time integration schemes called Linearly-Implicit Runge-Kutta-W (LIRK-W) methods. These schemes are based on an implicit-explicit approach which does not require a splitting of the right hand side and allow for arbitrary, time dependent, and stage varying approximations of the linear systems appearing in the method. Several formulations of LIRK-W schemes, each designed for specific approximation types, and their associated order condition theories are presented.

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