Roberts, StevenSandu, Adrian2022-02-272022-02-272022-01-19http://hdl.handle.net/10919/108889When applied to stiff, linear differential equations with time-dependent forcing, Runge-Kutta methods can exhibit convergence rates lower than predicted by the classical order condition theory. Commonly, this order reduction phenomenon is addressed by using an expensive, fully implicit Runge-Kutta method with high stage order or a specialized scheme satisfying additional order conditions. This work develops a flexible approach of augmenting an arbitrary Runge-Kutta method with a fully implicit method used to treat the forcing such as to maintain the classical order of the base scheme. Our methods and analyses are based on the general-structure additive Runge-Kutta framework. Numerical experiments using diagonally implicit, fully implicit, and even explicit Runge-Kutta methods confirm that the new approach elimi- nates order reduction for the class of problems under consideration, and the base methods achieve their theoretical orders of convergence.application/pdfenIn Copyrightmath.NAcs.NA65L04, 65L20Article - Refereed2022-02-27Sandu, Adrian [0000-0002-5380-0103]