通过最佳时间步长选择和非迭代缺陷校正提高Finite Difference格式的精度
Boosting the Accuracy of Finite Difference Schemes via Optimal Time Step Selection and Non-Iterative Defect Correction
摘要：
在这篇文章中，我们提出了一个简单的技术，用于提高精度的顺序的有限差分格式的不定常于偏微分方程的最佳选择的时间步长用于推进数值解和添加缺陷校正项在非迭代的方式。该技术的力量是它能够提取尽可能多的精度，尽可能从现有的有限差分格式，以最小的额外努力。通过简单的数值分析参数，我们解释了提高精度的起源，并估计所产生的数值方法的计算成本。我们证明了效用的最佳时间步长（OTS）的选择结合非迭代缺陷校正（NIDC）的几种不同类型的有限差分格式的一个或多个空间维度上的一系列经典的线性和半线性偏微分方程的规则和不规则域。
英文摘要：
In this article, we present a simple technique for boosting the order of accuracy of finite difference schemes for time dependent partial differential equations by optimally selecting the time step used to advance the numerical solution and adding defect correction terms in a non-iterative manner. The power of the technique is its ability to extract as much accuracy as possible from existing finite difference schemes with minimal additional effort. Through straightforward numerical analysis arguments, we explain the origin of the boost in accuracy and estimate the computational cost of the resulting numerical method. We demonstrate the utility of optimal time step (OTS) selection combined with non-iterative defect correction (NIDC) on several different types of finite difference schemes for a wide array of classical linear and semilinear PDEs in one and more space dimensions on both regular and irregular domains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
