论文标题
针对多步项应用的初始值问题的一般放松方法
General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes
论文作者
论文摘要
最近，已经开发了一种称为弛豫的方法，用于保留使用Runge-Kutta方法在初始值问题的数值解决方案中的正确演变。我们将这种方法推广到多步法方法，包括所有阶级或更高阶和许多其他类别方案的一般线性方法。在通用方程式（包括但不限于保守或耗散系统）的背景下，我们证明了由此产生的方法的有效放松参数和高阶精度的存在。该理论用几个数值示例进行了说明。
Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-Kutta methods. We generalize this approach to multistep methods, including all general linear methods of order two or higher, and many other classes of schemes. We prove the existence of a valid relaxation parameter and high-order accuracy of the resulting method, in the context of general equations, including but not limited to conservative or dissipative systems. The theory is illustrated with several numerical examples.
