One-sided direct event location techniques in the numerical solution of discontinuous differential systems

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• 作者：Luca Dieci ; Luciano Lopez
• 关键词：Event manifold ; Time reparametrization ; Runge Kutta methods ; Monotone integration ; 65L05 ; 34A36
• 刊名：BIT Numerical Mathematics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：55
• 期：4
• 页码：987-1003
• 全文大小：632 KB
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• 作者单位：Luca Dieci (1)
  Luciano Lopez (2)
  
  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA
  2. Dipartimento di Matematica, Universit谩 degli Studi di Bari 鈥淎ldo Moro鈥? Via E. Orabona 4, 70125, Bari, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Numeric Computing
  Mathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9125

文摘

In this paper, event location techniques for a differential system the solution of which is directed towards a manifold \(\varSigma \) defined as the 0-set of a smooth function \(h: \varSigma =\{x\in \mathbb {R}^n\,:\, h(x)=0 \}\) are considered. It is assumed that the exact solution trajectory hits \(\varSigma \) non-tangentially, and numerical techniques guaranteeing that the trajectory approaches \(\varSigma \) from one side only (i.e., does not cross it) are studied. Methods based on Runge Kutta schemes which arrive to \(\varSigma \) in a finite number of steps are proposed. The main motivation of this paper comes from integration of discontinuous differential systems of Filippov type, where location of events is of paramount importance. Keywords Event manifold Time reparametrization Runge Kutta methods Monotone integration