Homotopy-Based Methods in Water Engineering

Manotosh Kumbhakar, Vijay P. Singh

• Publisher: CRC Press
• Year: 2023
• Print ISBN: 9781032438214
• eBook ISBN: 9781000893397
• Topic: Tecnologia e ingegneria
• Subtopic: Matematica applicata

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

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Contents
• Preface
• About the Authors
• Part I: Introduction
• Part II: Algebraic/Transcendental Equations
• PART III Ordinary Differential Equations (Single and System)
• PART IV Partial Differential Equations (Single and System)
• Part V: Integro-Differential Equations
• Index