Numerical Solutions to Partial Differential Equations with Finite Difference Methods
暫譯: 有限差分法求解偏微分方程的數值解

Sun, Zhi-Zhong, Zhang, Qifeng, Gao, Guang-Hua

Numerical Solutions to Partial Differential Equations with Finite Difference Methods
  • 出版商: Springer
  • 出版日期: 2026-06-02
  • 售價: $3,240
  • 貴賓價: 9.5 折 $3,078
  • 語言: 英文
  • 頁數: 463
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 9819555620
  • ISBN-13: 9789819555628
  • 相關分類: 數值分析 Numerical-analysis

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

This book presents finite difference methods for three types of classical linear PDEs, three types of nonlinear PDEs and fractional PDEs. Specific topics cover two-point boundary value problems, elliptic equations, parabolic equations, hyperbolic equations, high-dimensional evolution equations, Schr\''{o}dinger equations, the Burgers' equation, the Korteweg-de Vries equation, and fractional diffusion-wave equations.

The book strives to achieve:

(a) Featured content. Thorough and dedicated presentations are provided for the finite difference methods.

(b) Scattered difficulty. Starting from a simple two-point boundary value problem for an ODE, authors introduce core concepts and analytical techniques of the finite difference methods, then apply them to handle with various partial differential equations.

(c) Emphasis on practicability. For each algorithm, provided numerical examples enable students to learn how to apply it and verify theoretical results with numerical outcomes.

The book is suitable for advanced undergraduate and beginning graduate students in applied mathematics and engineering.

商品描述(中文翻譯)

本書介紹了三種類型的經典線性偏微分方程（PDE）、三種類型的非線性偏微分方程以及分數偏微分方程的有限差分方法。具體主題涵蓋了二點邊值問題、橢圓方程、拋物方程、雙曲方程、高維演化方程、薛丁格方程、伯格斯方程、科爾特維克-德弗里斯方程以及分數擴散-波方程。

本書力求達成以下目標：

(a) 特色內容。對於有限差分方法提供徹底且專注的介紹。

(b) 難度分散。從一個簡單的常微分方程（ODE）二點邊值問題開始，作者介紹有限差分方法的核心概念和分析技術，然後將其應用於處理各種偏微分方程。

(c) 強調實用性。對於每個算法，提供的數值範例使學生能夠學習如何應用它並用數值結果驗證理論結果。

本書適合應用數學和工程領域的高年級本科生及初級研究生。

作者簡介

Zhi-Zhong Sun, Professor at the School of Mathematics, Southeast University. Sun was born in March 1963. He received his bachelor and master degree from Nanjing University in 1984 and 1987 respectively, and obtained his PhD from Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences in 1990. He engaged in the finite difference methods for the partial differential equations, especially the nonlinear evolutionary differential equations, fractional order differential equations.

Qifeng Zhang, Associate Professor at the Department of Mathematics, Zhejiang Sci-Tech University. Zhang was born in September 1987. He received his PhD from Huazhong University of Science and Technology in 2014. He visited Ecole Polytechnique Federale de Lausanne in 2020. His research interests are numerical analysis and simulation of nonlinear water wave equations and fractional order differential equations.

Guang-hua Gao, Associate Professor at the College of Science, Nanjing University of Posts and Telecommunications. Gao was born in November 1985. She obtained her PhD from Southeast University in 2012. She visited University of Macau in 2014. Her main research interest is numerical methods for partial differential equations.

作者簡介(中文翻譯)

Zhi-Zhong Sun，東南大學數學院教授。Sun於1963年3月出生。他於1984年和1987年分別獲得南京大學的學士和碩士學位，並於1990年獲得中國科學院數學與系統科學研究院的博士學位。他專注於偏微分方程的有限差分方法，特別是非線性演化微分方程和分數階微分方程。

Qifeng Zhang，浙江科技大學數學系副教授。Zhang於1987年9月出生。他於2014年獲得華中科技大學的博士學位。2020年，他曾訪問洛桑聯邦理工學院。他的研究興趣包括非線性水波方程和分數階微分方程的數值分析與模擬。

Guang-hua Gao，南京郵電大學科學學院副教授。Gao於1985年11月出生。她於2012年獲得東南大學的博士學位。2014年，她曾訪問澳門大學。她的主要研究興趣是偏微分方程的數值方法。

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