Linearly implicit Runge-Kutta methods and approximate matrix factorization.
The paper deals with the analysis of the use of approximate matrix factorization for solving the stage equations in linearly implicit Runge-Kutta methods. The authors derive a correction which allows an order two and preserve the main stability properties of the linearly implicit Runge-Kutta method. This is illustrated on the taxis-diffusion-reaction systems from mathematical biology.
scientific article; zbMATH DE number 2160258