论文标题
一类耗散系统的均匀精确数值方案
Uniformly accurate numerical schemes for a class of dissipative systems
论文作者
论文摘要
我们考虑了一类放松问题，以混合缓慢和快速的变化，这些变化可以描述种群动态模型或双曲线系统，并具有变化的刚度（从非Stift到强烈耗散），并通过将此问题分解为原始刚度的微型麦克罗系统，从而开发出多尺度方法。我们表明，可以使用标准的显式数值方案以统一的精度顺序模拟这个新问题。换句话说，可以通过与刚度无关的成本（又称均匀成本）来解决微麦克罗问题，从而使误差也均匀。该方法成功地应用于有或没有非线性的两个双曲线系统，并被证明可以避免降级降低现象。
We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale method by decomposing this problem into a micro-macro system where the original stiffness is broken. We show that this new problem can therefore be simulated with a uniform order of accuracy using standard explicit numerical schemes. In other words, it is possible to solve the micro-macro problem with a cost independent of the stiffness (a.k.a. uniform cost), such that the error is also uniform. This method is successfully applied to two hyperbolic systems with and without non-linearities, and is shown to circumvent the phenomenon of order reduction.
