Contractivity/monotonicity for additive Runge–Kutta methods: Inner product norms

Space discretization of some time dependent partial differential equations give rise to ordinary differential equations containing additive terms with different stiffness properties. In these situations, additive Runge–Kutta (ARK) methods are used. The aim of this paper is the study of contractivity and monotonicity properties for ARK methods when the used norm is an inner product norm. Stepsize restrictions for contractivity and monotonicity can be obtained in terms of problem and method parameters. Some ARK methods from the literature are analyzed.