Fractional-step Runge–Kutta methods: Representation and linear stability analysis

Fractional-step methods are a popular and powerful divide-and-conquer approach for the numerical solution of differential equations. When integrators fractional steps Runge--Kutta methods, such can be written as generalized additive (GARK) thus representation analysis done through GARK framework. We show how general Butcher tableau linear stability related to coefficients splitting method, individual sub-integrators, order in which they applied. use this framework explain some observations literature about fractional-step choice applied, role played by negative method.