论文标题
高阶半密度多步法方法用于时间依赖的部分微分方程
High order semi-implicit multistep methods for time dependent partial differential equations
论文作者
论文摘要
我们考虑了半图形线性多步法方法的构建，这些方法可以应用于时间依赖的PDE，其中不可能以添加形式的比例分离（通常用于隐式解释（IMEX）方法）。如Boscarino，Filbet和Russo（2016）所示，用于runge-kutta方法，这些半平滑技术具有很大的灵活性，并且在许多情况下，允许构建简单的线性隐含方案，而无需迭代式求解器。在这项工作中，我们为建造高阶半密度线性多步构方法的构建开发了一个一般设置，并分析了其稳定性线性对流扩散方程以及在强稳定性保留（SSP）方法的设置中的稳定性。我们的发现在几个示例中得到了证明，包括非线性反应扩散和对流扩散问题。
We consider the construction of semi-implicit linear multistep methods which can be applied to time dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As shown in Boscarino, Filbet and Russo (2016) for Runge-Kutta methods, these semi-implicit techniques give a great flexibility, and allows, in many cases, the construction of simple linearly implicit schemes with no need of iterative solvers. In this work we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype linear advection-diffusion equation and in the setting of strong stability preserving (SSP) methods. Our findings are demonstrated on several examples, including nonlinear reaction-diffusion and convection-diffusion problems.
