A Concise Introduction to Geometric Numerical Integration
暫譯: 幾何數值積分簡明導論
Blanes, Sergio, Casas, Fernando
- 出版商: CRC
- 出版日期: 2025-11-19
- 售價: $4,770
- 貴賓價: 9.5 折 $4,532
- 語言: 英文
- 頁數: 233
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 1032862467
- ISBN-13: 9781032862460
-
相關分類:
數值分析 Numerical-analysis
海外代購書籍(需單獨結帳)
商品描述
"This book is highly recommended for graduate students, postgraduate researchers, and researchers interested in beginning study in the field of geometric numerical integration."
--Mathematical Reviews
A Concise Introduction to Geometric Numerical Integration, Second Edition presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration.
Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the most significant ideas, methods, and applications. Readers can reproduce the figures and results given in the text using the MATLAB(R) programs and model files available online.
New to the second edition
- Focus on single-step methods for solving differential equations.
- Full-scale rewrite of Chapter 3, with a new introduction and a more comprehensive treatment of non-autonomous systems and the processing technique.
- New section dedicated to multi-product methods in Chapter 4, and a mention the class of Crouch-Grossman and positivity-preserving integrators.
- A fresh introduction and a more detailed discussion of splitting and composition methods with complex coefficients in Chapter 6.
- A brand-new Chapter 7, showcasing some compelling applications where geometric integrators are now being used.
- Redesigned figures throughout, with improved their clarity and readability. The codes for generating them are provided at the website accompanying the book.
- New exercises, as well as an enhanced list of bibliographic references.
商品描述(中文翻譯)
這本書非常推薦給研究生、研究所研究人員以及對幾何數值積分領域有興趣的研究者。
-- *數學評論*
**《幾何數值積分簡明導論（第二版）》** 提出了幾何積分器的主要主題、技術和應用，適合已經熟悉解決微分方程的數值工具的數學、物理、天文和化學研究者。它還提供了一個從傳統的微分方程數值分析訓練到理解最近的高級研究文獻的橋樑，這些文獻涉及數值幾何積分。
這本入門書籍對來自不同背景的研究者和研究生都很友好，幫助讀者迅速掌握最重要的概念、方法和應用。讀者可以使用在線提供的 MATLAB(R) 程式和模型檔案重現文本中的圖形和結果。
**第二版的新內容**
- 專注於解決微分方程的單步法。
- 第三章進行全面重寫，新增介紹並更全面地處理非自治系統及其處理技術。
- 第四章新增專門針對多產品方法的部分，並提及 Crouch-Grossman 類別及保持正性的積分器。
- 第六章提供全新的介紹，並對具有複數係數的分裂和組合方法進行更詳細的討論。
- 全新第七章，展示一些幾何積分器目前正在使用的引人注目的應用。
- 全書的圖形重新設計，提高了清晰度和可讀性。生成這些圖形的程式碼在書籍附帶的網站上提供。
- 新增練習題，以及增強的文獻參考列表。
作者簡介
Sergio Blanes is a Professor of Applied Mathematics at Universitat Politècnica de València, Spain. He earned his PhD in Theoretical Physics from the Universitat de València in 1998. Following this, he held postdoctoral research positions at the University of Cambridge, the University of Bath, and the University of California, San Diego. In 2002, he was awarded a Ramón y Cajal Research Fellowship. He was also a visiting researcher at the Isaac Newton Institute in 2019. His research interests include geometric numerical integration and computational mathematics and physics.
Fernando Casas is a Professor of Applied Mathematics at Universitat Jaume I in Castellón, Spain. He has served as a Visiting Research Associate at the University of Maryland, College Park, and as a Temporary Assistant Research Scientist at Texas A&M University at Qatar. In 2018, he held the Lebesgue Chair (Senior Position) at the Centre Henri Lebesgue, Université de Rennes. His primary research interests lie in the numerical analysis of differential equations and geometric numerical integration.
作者簡介(中文翻譯)
Sergio Blanes 是西班牙瓦倫西亞理工大學的應用數學教授。他於1998年在瓦倫西亞大學獲得理論物理博士學位。隨後，他在劍橋大學、巴斯大學和加州大學聖地亞哥分校擔任博士後研究職位。2002年，他獲得了 Ramón y Cajal 研究獎學金。他在2019年也曾擔任艾薩克·牛頓研究所的訪問研究員。他的研究興趣包括幾何數值積分和計算數學與物理。
Fernando Casas 是西班牙卡斯特利翁的哈梅一世大學的應用數學教授。他曾擔任馬里蘭大學（College Park）的訪問研究助理，以及卡塔爾德州農工大學的臨時助理研究科學家。2018年，他在亨利·勒貝格中心（Centre Henri Lebesgue），雷恩大學擔任勒貝格講座（高級職位）。他的主要研究興趣在於微分方程的數值分析和幾何數值積分。
