Kumbhakar M., Singh V.P. Homotopy-Based Methods in Water Engineering

CRC Press, 2023. — 471 p. — ISBN 978-1032438215.Гомотопические методы в гидротехнике
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.Preface
PART I Introduction
Chapter 1 Introduction
Chapter 2 Basic Concepts
PART II Algebraic/Transcendental Equations
Chapter 3 Numerical Solutions for the Colebrook Equation
PART III Ordinary Differential Equations (Single and System)
Chapter 4 Velocity Distribution in Smooth Uniform Open-Channel Flow
Chapter 5 Sediment Concentration Distribution in Open-Channel Flow
Chapter 6 Richards Equation under Gravity-Driven Infiltration and Constant Rainfall Intensity
Chapter 7 Error Equation for Unsteady Uniform Flow
Chapter 8 Spatially Varied Flow Equations
Chapter 9 Modeling of a Nonlinear Reservoir
Chapter 10 Nonlinear Muskingum Method for Flood Routing
Chapter 11 Velocity and Sediment Concentration Distribution in Open-Channel Flow
PART IV Partial Differential Equations (Single and System)
Chapter 12 Unsteady Confined Radial Ground-Water Flow Equation
Chapter 13 Series Solutions for Burger’s Equation
Chapter 14 Diffusive Wave Flood Routing Problem with Lateral Inflow
Chapter 15 Kinematic Wave Equation
Chapter 16 Multispecies Convection-Dispersion Transport Equation with Variable Parameters
PART V Integro-Differential Equations
Chapter 17 Absorption Equation in Unsaturated Soil