论文标题
一个新的有效的显式递延校正框架：分析和对双曲线PDE和适应性的应用
A new efficient explicit Deferred Correction framework: analysis and applications to hyperbolic PDEs and adaptivity
论文作者
论文摘要
递延校正（DEC）是一个迭代过程，其特征是每次迭代的精度提高，可用于设计ODES系统的数值方法。这种框架的主要优点是自动获取任意高阶方法的方法，可以将其放入runge-kutta（RK）表单中。缺点是相对于最常用的RK方法的较大计算成本。为了降低这种成本，在明确的环境中，我们提出了一个有效的修改：我们在迭代之间介绍了插值过程，从而降低了与低阶相关的计算成本。我们提供了新的修改方法的屠夫tableaux，我们研究了它们的稳定性，表明在某些情况下，计算优势不会影响稳定性。新颖的修饰的灵活性允许对PDE的非平凡应用和自适应方法的构建。引入方法的良好性能在ODE和PDE上下文中的几个基准上进行了广泛的测试。
The Deferred Correction (DeC) is an iterative procedure, characterized by increasing accuracy at each iteration, which can be used to design numerical methods for systems of ODEs. The main advantage of such framework is the automatic way of getting arbitrarily high order methods, which can be put in Runge--Kutta (RK) form. The drawback is the larger computational cost with respect to the most used RK methods. To reduce such cost, in an explicit setting, we propose an efficient modification: we introduce interpolation processes between the DeC iterations, decreasing the computational cost associated to the low order ones. We provide the Butcher tableaux of the new modified methods and we study their stability, showing that in some cases the computational advantage does not affect the stability. The flexibility of the novel modification allows nontrivial applications to PDEs and construction of adaptive methods. The good performances of the introduced methods are broadly tested on several benchmarks both in ODE and PDE contexts.
