This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class of integrators are composition methods, in which one or several low-order schemes are composed to construct higher-order numerical approximations to the exact solution. We analyse in detail the order conditions that have to be satisfied by these classes of methods to achieve a given order, and provide some insight about their qualitative properties in connection with geometric numerical integration and the treatment of highly oscillatory problems. Since splitting methods have received considerable attention in the realm of partial differential equations, we also cover this subject in the present survey, with special attention to parabolic equations and their problems. An exhaustive list of methods of different orders is collected and tested on simple examples. Finally, some applications of splitting methods in different areas, ranging from celestial mechanics to statistics, are also provided.

Sergio Blanes

Fernando Casas

Ander Murua

Acta Numerica

ACTA NUMERICA 是过去两年在 MATHSCINET 中被引用次数最多的期刊。其年度评论文章集包括数值分析和科学计算领域领先研究人员的调查论文。这些论文概述了最近的进展，并提供了最先进的技术和分析。涵盖数值分析的广度，文章以各级研究人员可以访问的风格编写，可以作为高级教具。广泛的学科领域包括线性​​代数、优化、常微分方程和偏微分方程、近似理论、随机分析和非线性动力系统中的计算方法，以及计算技术在科学和工程中的应用以及数值方法的数学理论。

Acta Numerica is the most cited journal in MATHSCINET over the past two years. Its annual collection of review articles features survey papers from leading researchers in the fields of numerical analysis and scientific computing. These papers outline recent advancements and provide state-of-the-art techniques and analyses. Covering a broad range of topics in numerical analysis, the articles are written in a style accessible to researchers at all levels and can serve as advanced teaching materials. The wide-ranging subjects include linear algebra, optimization, ordinary and partial differential equations, approximation theory, stochastic analysis, and computational methods in nonlinear dynamical systems, as well as the application of computational techniques in science and engineering and the mathematical theory of numerical methods.

《Acta Numerica》是过去两年在MATHSCINET中被引用次数最多的期刊。其年度评论文章集汇集了数值分析和科学计算领域的领先研究人员的调查论文。这些论文概述了最近的研究进展，并提供了最先进的技术和分析。涵盖数值分析的广泛主题，文章以各级研究人员都能理解的风格撰写，适合作为高级教学材料。相关学科包括线性代数、优化、常微分方程和偏微分方程、近似理论、随机分析以及非线性动力系统中的计算方法，同时也涉及计算技术在科学和工程中的应用及数值方法的数学理论。

Category	Quartile
数学	1
数学, 数学	1

Splitting methods for differential equations

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