Numerical Methods for Initial Value Problems in Physics
Guzmán, Francisco S.
- 出版商: Springer
- 出版日期: 2024-08-24
- 售價: $2,980
- 貴賓價: 9.5 折 $2,831
- 語言: 英文
- 頁數: 357
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031335589
- ISBN-13: 9783031335587
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相關分類:
物理學 Physics
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相關主題
商品描述
This textbook is a comprehensive overview of the construction, implementation, and application of important numerical methods for the solution of Initial Value Problems (IVPs). Beginning with IVPs involving Ordinary Differential Equations (ODEs) and progressing to problems with Partial Differential Equations (PDEs) in 1+1 and 3+1 dimensions, it provides readers with a clear and systematic progression from simple to complex concepts.
The numerical methods selected in this textbook can solve a considerable variety of problems and the applications presented cover a wide range of topics, including population dynamics, chaos, celestial mechanics, geophysics, astrophysics, and more. Each chapter contains a variety of solved problems and exercises, with code included. These examples are designed to motivate and inspire readers to delve deeper into the state-of-the-art problems in their own fields. The code is written in Fortran 90, in a library-free style, making them easy to program and efficient to run. The appendix also includes the same code in C++, making the book accessible to a variety of programming backgrounds.
At the end of each chapter, there are brief descriptions of how the methods could be improved, along with one or two projects that can be developed with the methods and codes described. These projects are highly engaging, from synchronization of chaos and message encryption to gravitational waves emitted by a binary system and non-linear absorption of a scalar field. With its clear explanations, hands-on approach, and practical examples, this textbook is an essential resource for advanced undergraduate and graduate students who want to the learn how to use numerical methods to tackle challenging problems.
商品描述(中文翻譯)
這本教科書全面概述了重要數值方法的建構、實施和應用,以解決初始值問題(IVPs)。從涉及常微分方程(ODEs)的初始值問題開始,逐步進展到具有偏微分方程(PDEs)的1+1和3+1維問題,為讀者提供了從簡單到複雜概念的清晰和系統的進展。
本教科書中選擇的數值方法能夠解決各種問題,所呈現的應用涵蓋了廣泛的主題,包括人口動態、混沌、天體力學、地球物理學、天體物理學等。每一章都包含多種已解決的問題和練習,並附有程式碼。這些範例旨在激勵和啟發讀者深入探索自己領域中的尖端問題。程式碼使用Fortran 90編寫,採用無庫存的風格,使其易於編程且運行效率高。附錄中還包括相同的C++程式碼,使本書對各種程式設計背景的讀者都能夠輕鬆使用。
在每一章的結尾,簡要描述了如何改進這些方法,並附上一到兩個可以利用所描述的方法和程式碼開發的專案。這些專案非常引人入勝,從混沌的同步和訊息加密到由雙星系統發出的引力波以及標量場的非線性吸收。憑藉其清晰的解釋、實踐的方法和實用的範例,這本教科書是希望學習如何使用數值方法解決挑戰性問題的高年級本科生和研究生的重要資源。
作者簡介
Dr. Francisco S. Guzmán serves as a Professor for the Institute of Physics and Mathematics at Universidad Michoacana de San Nicolás de Hidalgo in Morelia, Mexico. In 2000, he received his PhD in Physics from The Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV) in Mexico City, Mexico. His research interest lies in the numerical solutions of partial differential equations, with applications to hydrodynamics, plasmas, Bose-Einstein condensates, complex fluids, diffusion systems, and populations. He has directed 18 undergraduate, 11 masters, and 6 doctoral theses, one of which was the winner of the 2017 Weizmann Award for Best PhD Thesis in Exact Sciences, a distinction awarded annually by the Mexican Academy of Sciences. Dr. Guzmán has published 108 articles in international journals and conference proceedings, authored 5 book chapters, and received over 2000 citations.
作者簡介(中文翻譯)
Dr. Francisco S. Guzmán 擔任墨西哥莫雷利亞的米卻肯州立大學物理與數學研究所教授。2000年,他在墨西哥城的國立工業學院高級研究中心 (CINVESTAV) 獲得物理學博士學位。他的研究興趣在於偏微分方程的數值解,應用於流體力學、等離子體、玻色-愛因斯坦凝聚、複雜流體、擴散系統和人口動態。他指導了18篇本科論文、11篇碩士論文和6篇博士論文,其中一篇獲得2017年魏茲曼獎最佳精確科學博士論文獎,該獎項由墨西哥科學院每年頒發。Guzmán 博士在國際期刊和會議論文集中發表了108篇文章,撰寫了5章書籍,並獲得超過2000次引用。