| 期刊全称 | B-Series | | 期刊简称 | Algebraic Analysis o | | 影响因子2023 | John C. Butcher | | 视频video | | | 发行地址 | A thorough introduction to B-series, written by its originator.Contains a self-contained analysis of Runge-Kutta methods.Includes a detailed study of trees and related constructs.Applies B-series to g | | 学科分类 | Springer Series in Computational Mathematics | | 图书封面 |  | | 影响因子 | B-series, also known as Butcher series, are an algebraic tool for analysing solutions to ordinary differential equations, including approximate solutions. Through the formulation and manipulation of these series, properties of numerical methods can be assessed. Runge–Kutta methods, in particular, depend on B-series for a clean and elegant approach to the derivation of high order and efficient methods. However, the utility of B-series goes much further and opens a path to the design and construction of highly accurate and efficient multivalue methods. .This book offers a self-contained introduction to B-series by a pioneer of the subject. After a preliminary chapter providing background on differential equations and numerical methods, a broad exposition of graphs and trees is presented. This is essential preparation for the third chapter, in which the main ideas of B-series are introduced and developed. In chapter four, algebraic aspects are further analysed in the context of integration methods, a generalization of Runge–Kutta methods to infinite index sets. Chapter five, on explicit and implicit Runge–Kutta methods, contrasts the B-series and classical approaches. Chapter six, on | | Pindex | Book 2021 |
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发表于 2025-3-21 18:22:21
