LIRK-W: Linearly-implicit Runge-Kutta methods with approximate matrix factorization
For researchers in numerical time integration, this provides a flexible framework that relaxes constraints on linear system approximations, but the contribution is incremental as it extends existing IMEX-RK methods.
This paper introduces LIRK-W methods, a new class of linearly implicit time integration schemes that allow arbitrary, time-dependent, and stage-varying approximations of linear systems, with order condition theories for multiple formulations.
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.