Homotopy-Based Methods in Water Engineering

<p>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. <i>Homotopy-Based Methods in Water Engineering </i>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.</p><p>Features:</p><ul> <p> </p> <li>Provides analytical treatments to some key problems in water engineering</li> </ul><ul> <p> </p> <li>Describes the applicability of homotopy-based methods for solving nonlinear equations particularly differential equations</li> </ul><ul> <p> </p> <li>Compares different approaches in dealing with issues of nonlinearity</li> </ul>