Homotopy-Based Methods in Water Engineering
暫譯: 水工程中的同倫方法

Kumbhakar, Manotosh, Singh, Vijay P.

Homotopy-Based Methods in Water Engineering

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商品描述

Most complex physical phenomena can be described by nonlinear equations, specifically, differential equations. In water engineering, nonlinear differential equations play a vital role in modeling physical processes. Analytical solutions to strong nonlinear problems are not easily tractable, and existing techniques are problem-specific and applicable for specific types of equations. Exploring the concept of homotopy from topology, different kinds of homotopy-based methods have been proposed for analytically solving nonlinear differential equations, given by approximate series solutions. Homotopy-Based Methods in Water Engineering attempts to present the wide applicability of these methods to water engineering problems. It solves all kinds of nonlinear equations, namely algebraic/transcendental equations, ordinary differential equations (ODEs), systems of ODEs, partial differential equations (PDEs), systems of PDEs, and integro-differential equations using the homotopy-based methods. The content of the book deals with some selected problems of hydraulics of open-channel flow (with or without sediment transport), groundwater hydrology, surface-water hydrology, general Burger's equation, and water quality.

Features:

  • Provides analytical treatments to some key problems in water engineering

  • Describes the applicability of homotopy-based methods for solving nonlinear equations, particularly differential equations

  • Compares different approaches in dealing with issues of nonlinearity

商品描述(中文翻譯)

大多數複雜的物理現象可以用非線性方程來描述，特別是微分方程。在水利工程中，非線性微分方程在建模物理過程中扮演著至關重要的角色。強非線性問題的解析解並不容易獲得，現有的技術通常是針對特定問題和特定類型的方程。從拓撲學中探索同倫（homotopy）的概念，已提出不同類型的基於同倫的方法來解析解非線性微分方程，這些解通常以近似級數解的形式給出。《水利工程中的同倫方法》試圖展示這些方法在水利工程問題中的廣泛適用性。它使用基於同倫的方法解決各種非線性方程，即代數/超越方程、常微分方程（ODEs）、常微分方程系統、偏微分方程（PDEs）、偏微分方程系統以及積分微分方程。該書的內容涉及一些選定的開放渠道流動的水力學問題（有或沒有沉積物運輸）、地下水水文學、地表水水文學、一般的Burger方程以及水質問題。

特色：
- 提供對水利工程中一些關鍵問題的解析處理
- 描述基於同倫的方法在解決非線性方程，特別是微分方程方面的適用性
- 比較處理非線性問題的不同方法

作者簡介

Manotosh Kumbhakar is a Postdoctoral Researcher at National Taiwan University, Tawan. Previously, he was a Postdoctoral Research Associate at Texas A&M University, USA, from 2020-2021. He specializes in entropy theory, mechanics of sediment transport, and semi-analytical methods. Dr. Manotosh has published several papers in reputed international journals.

Vijay P. Singh, Ph.D., D.Sc., D. Eng. (Hon.), Ph.D. (Hon..), P.E., P.H., Hon. D. WRE, Dist.M. ASCE, NAE, is a Distinguished Professor, a Regents Professor, and Caroline & William N. Lehrer Distinguished Chair in Water Engineering in Department of Biological and Agricultural Engineering and Zachry Department of Civil & Environmental Engineering at Texas A&M University. He specializes in surface-water hydrology, groundwater hydrology, hydraulics, irrigation engineering, environmental and water resources engineering, entropy theory, and copula theory. Professor Singh has published extensively and has received 110 national and international awards, including three honorary doctorates. He is a member of National Academy of Engineering, and a fellow or member of 12 international engineering/science academies.

作者簡介(中文翻譯)

Manotosh Kumbhakar 是國立台灣大學的博士後研究員。之前，他於 2020 至 2021 年在美國德州農工大學擔任博士後研究助理。他專精於熵理論、沉積物運輸力學及半解析方法。Manotosh 博士已在多本知名國際期刊上發表了數篇論文。

Vijay P. Singh 博士、科學博士、榮譽工程博士、榮譽博士、專業工程師、公共衛生博士、榮譽水資源工程師、ASCE 傑出會員、NAE 會員，是德州農工大學生物與農業工程系及扎克里土木與環境工程系的傑出教授、董事教授及 Caroline & William N. Lehrer 水工程傑出講座教授。他專精於地表水水文學、地下水水文學、水力學、灌溉工程、環境與水資源工程、熵理論及聯合分布理論。Singh 教授發表了大量研究成果，並獲得 110 項國內外獎項，包括三個榮譽博士學位。他是美國國家工程院的會員，並且是 12 個國際工程/科學學院的院士或會員。

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