Stage value predictors for additive and partitioned Runge–Kutta methods

Additive and partitioned Runge–Kutta methods are widely used for the numerical integration of some special ODEs. They usually involve the numerical solution of nonlinear systems that require starting values as accurate as possible. In this paper we consider stage value predictors for these kind of methods. First, we deal with partitioned Runge–Kutta methods. The results obtained are transferred to additive Runge–Kutta methods. The theory developed is used to construct starting values for the Lobatto IIIA–IIIB methods and some IMEX methods from the literature. Some numerical results show that the use of the stage value predictors considered in this paper reduces the number of iterations per step and hence the computational cost.