Homotopy-Based Methods in Water Engineering

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

大多數複雜的物理現象可以用非線性方程式，特別是微分方程式來描述。在水利工程中，非線性微分方程式在建模物理過程中起著重要作用。強非線性問題的解析解不容易處理，現有的技術是針對特定類型的方程式而設計的，並且只適用於特定問題。從拓撲學中探索同伦的概念，提出了不同種類的基於同伦的方法，用於以近似級數解析解非線性微分方程式。《水利工程中的同伦方法》試圖展示這些方法在水利工程問題中的廣泛應用性。它使用基於同伦的方法解決各種非線性方程式，包括代數/超越方程式、常微分方程式（ODEs）、ODE系統、偏微分方程式（PDEs）、PDE系統和积分微分方程式。本書的內容涉及開渠流（帶或不帶沉積物輸送）、地下水水文學、地表水水文學、一般的Burger方程和水質等一些選定的問題。

特點：
- 對水利工程中的一些關鍵問題提供解析處理
- 描述了基於同伦的方法在解決非線性方程式，特別是微分方程式方面的應用性
- 比較了處理非線性問題的不同方法

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.

Manotosh Kumbhakar是國立臺灣大學的博士後研究員。之前，他在2020年至2021年間擔任美國德克薩斯農工大學的博士後研究員。他專攻於熵理論、沉積物運移力學和半解析方法。Manotosh博士在知名國際期刊上發表了多篇論文。

Vijay P. Singh博士是德克薩斯農工大學生物與農業工程系和Zachry土木與環境工程系的傑出教授、校董教授和Caroline & William N. Lehrer水利工程著名講座教授。他專攻於地表水水文學、地下水水文學、水力學、灌溉工程、環境和水資源工程、熵理論和copula理論。Singh教授廣泛發表論文，並獲得了110項國家和國際獎項，包括三個榮譽博士學位。他是國家工程學院的成員，也是12個國際工程/科學學院的會士或成員。