Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

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• 作者：Winfried Auzinger ; Harald Hofstätter ; David Ketcheson…
• 关键词：Evolution equations ; Splitting methods ; Free Lie algebra ; Order conditions ; Local error ; Embedded methods
• 刊名：BIT Numerical Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：57
• 期：1
• 页码：55-74
• 全文大小：517KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Numeric Computing; Mathematics, general;
• 出版者：Springer Netherlands
• ISSN：1572-9125
• 卷排序：57

文摘

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.