  When 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 eliminates order
reduction for the class of problems under consideration, and the base methods
achieve their theoretical orders of convergence.
