Starting algorithms for low stage order RKN methods
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Are high order variable step equistage initializers better than standard starting algorithms?
Journal of Computational and Applied Mathematics
Stage value predictors for additive and partitioned Runge-Kutta methods
Applied Numerical Mathematics
Time-step selection algorithms: adaptivity, control, and signal processing
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
ACM Transactions on Mathematical Software (TOMS)
An Efficient Fourth Order Implicit Runge-Kutta Algorithm for Second Order Systems
Computer Mathematics
A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations
Journal of Computational Physics
Stage value predictors for additive and partitioned Runge--Kutta methods
Applied Numerical Mathematics
Time-step selection algorithms: Adaptivity, control, and signal processing
Applied Numerical Mathematics
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The prediction of stage values in implicit Runge--Kutta methods is important both for overall efficiency as well as for the design of suitable control strategies for the method. The purpose of this paper is to construct good stage value predictors for implicit methods and to verify their behavior in practical computations. We show that for stiffly accurate methods of low stage order it is necessary to use several predictors. In other words, a continuous extension for the method will not yield the best results. We also investigate how to gain additional efficiency in the Newton iterations used to correct the prediction error. This leads to new control strategies with respect to refactorization of Jacobians that seek to globally minimize total work per unit time of integration.