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Methods for Constructing Exact Solutions of Partial Differential Equations

2006-06-18 Technology & Engineering
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Release : 2006-06-18
Genre : Technology & Engineering
Kind : eBook
Book Rating : 657/5 ( reviews)

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Book Synopsis Methods for Constructing Exact Solutions of Partial Differential Equations by : Sergey V. Meleshko

Download or read book Methods for Constructing Exact Solutions of Partial Differential Equations written by Sergey V. Meleshko. This book was released on 2006-06-18. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

Methods for Constructing Exact Solutions of Partial Differential Equations

2005-09-16 Mathematics
Download Methods for Constructing Exact Solutions of Partial Differential Equations PDF Online Free

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Release : 2005-09-16
Genre : Mathematics
Kind : eBook
Book Rating : 601/5 ( reviews)

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Book Synopsis Methods for Constructing Exact Solutions of Partial Differential Equations by : Sergey V. Meleshko

Download or read book Methods for Constructing Exact Solutions of Partial Differential Equations written by Sergey V. Meleshko. This book was released on 2005-09-16. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics

2006-11-02 Mathematics
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Release : 2006-11-02
Genre : Mathematics
Kind : eBook
Book Rating : 626/5 ( reviews)

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Book Synopsis Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics by : Victor A. Galaktionov

Download or read book Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics written by Victor A. Galaktionov. This book was released on 2006-11-02. Available in PDF, EPUB and Kindle. Book excerpt: Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics

2006-11-02 Mathematics
Download Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics PDF Online Free

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Release : 2006-11-02
Genre : Mathematics
Kind : eBook
Book Rating : 631/5 ( reviews)

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Book Synopsis Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics by : Victor A. Galaktionov

Download or read book Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics written by Victor A. Galaktionov. This book was released on 2006-11-02. Available in PDF, EPUB and Kindle. Book excerpt: Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.

Separation of Variables and Exact Solutions to Nonlinear PDEs

2021-09-19 Mathematics
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Release : 2021-09-19
Genre : Mathematics
Kind : eBook
Book Rating : 63X/5 ( reviews)

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Book Synopsis Separation of Variables and Exact Solutions to Nonlinear PDEs by : Andrei D. Polyanin

Download or read book Separation of Variables and Exact Solutions to Nonlinear PDEs written by Andrei D. Polyanin. This book was released on 2021-09-19. Available in PDF, EPUB and Kindle. Book excerpt: Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations (PDEs). It also presents the direct method of symmetry reductions and its more general version. In addition, the authors describe the differential constraint method, which generalizes many other exact methods. The presentation involves numerous examples of utilizing the methods to find exact solutions to specific nonlinear equations of mathematical physics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology, and other disciplines are studied. Particular attention is paid to nonlinear equations of a reasonably general form that depend on one or several arbitrary functions. Such equations are the most difficult to analyze. Their exact solutions are of significant practical interest, as they are suitable to assess the accuracy of various approximate analytical and numerical methods. The book contains new material previously unpublished in monographs. It is intended for a broad audience of scientists, engineers, instructors, and students specializing in applied and computational mathematics, theoretical physics, mechanics, control theory, chemical engineering science, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on partial differential equations, equations of mathematical physics, and methods of mathematical physics, for delivering special courses and for practical training.

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