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引用次数: 0
摘要
我们提出了一种通过多指数概念研究一维常微分方程数值方法的新方法。其主要思想是用多指数取代布彻 B $B$ 系列中的有根树。后者是最近在描述奇异随机偏微分方程解时引入的。从根树上进行组合转换,可以压缩数值方案的描述。此外,这种多指数 B $B$ 序列唯一地描述了一维局部和仿射等变映射的泰勒展开。
We propose a novel way to study numerical methods for ordinary differential equations in one dimension via the notion of multi-indice. The main idea is to replace rooted trees in Butcher's -series by multi-indices. The latter were introduced recently in the context of describing solutions of singular stochastic partial differential equations. The combinatorial shift away from rooted trees allows for a compressed description of numerical schemes. Furthermore, such multi-indices -series uniquely characterize the Taylor expansion of 1-dimensional local and affine equivariant maps.
期刊介绍:
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.