论文标题
消除与天线方法的线性相关ODE的订单降低
Eliminating Order Reduction on Linear, Time-Dependent ODEs with GARK Methods
论文作者
论文摘要
当应用于僵硬的线性微分方程与时间依赖性强迫时，runge-kutta方法的收敛速率可能低于经典条件理论的预测。通常，通过使用具有高舞台秩序或满足其他订单条件的专门方案的昂贵，完全隐含的runge-kutta方法来解决这种降低现象。这项工作开发了一种灵活的方法，即使用一种完全隐式的方法来增强任意runge-kutta方法，用于处理强迫，例如维护基本方案的经典顺序。我们的方法和分析基于一般结构加性runge-kutta框架。使用对角线隐式，完全隐式甚至明确的runge-kutta方法进行的数值实验证实，新方法消除了所考虑的问题类别的秩序降低，而基本方法达到了其理论融合顺序。
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.
