Separation Of Variables And Exact Solutions To Nonlinear Pdes

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Separation of Variables and Exact Solutions to Nonlinear PDEs

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 1000463664
Total Pages : 349 pages
Book Rating : 4.0/5 (4 download)

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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 and published by CRC Press. This book was released on 2021-09-20 with total page 349 pages. 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 The book contains new material previously unpublished in monographs.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.

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

Author : Victor A. Galaktionov
Publisher : CRC Press
ISBN 13 : 9781420011623
Total Pages : 528 pages
Book Rating : 4.0/5 (116 download)

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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 and published by CRC Press. This book was released on 2006-11-02 with total page 528 pages. 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.

Solving Nonlinear Partial Differential Equations with Maple and Mathematica

Author : Inna Shingareva
Publisher : Springer Science & Business Media
ISBN 13 : 370910517X
Total Pages : 357 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Solving Nonlinear Partial Differential Equations with Maple and Mathematica by : Inna Shingareva

Download or read book Solving Nonlinear Partial Differential Equations with Maple and Mathematica written by Inna Shingareva and published by Springer Science & Business Media. This book was released on 2011-07-24 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).

Separation of Variables and Exact Solutions to Nonlinear PDEs

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 100046363X
Total Pages : 402 pages
Book Rating : 4.0/5 (4 download)

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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 and published by CRC Press. This book was released on 2021-09-19 with total page 402 pages. 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.

Partial Differential Equations

Author : Walter A. Strauss
Publisher : John Wiley & Sons
ISBN 13 : 0470054565
Total Pages : 467 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Partial Differential Equations by : Walter A. Strauss

Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Nonlinear Partial Differential Equations in Engineering

Author : W. F. Ames
Publisher : Elsevier
ISBN 13 : 1483222926
Total Pages : 526 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Nonlinear Partial Differential Equations in Engineering by : W. F. Ames

Download or read book Nonlinear Partial Differential Equations in Engineering written by W. F. Ames and published by Elsevier. This book was released on 2016-06-03 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Partial Differential Equations in Engineering discusses methods of solution for nonlinear partial differential equations, particularly by using a unified treatment of analytic and numerical procedures. The book also explains analytic methods, approximation methods (such as asymptotic processes, perturbation procedures, weighted residual methods), and specific numerical procedures associated with these equations. The text presents exact methods of solution including the quasi-linear theory, the Poisson-Euler-Darboux equation, a general solution for anisentropic flow, and other solutions obtained from ad hoc assumptions. The book explores analytic methods such as an ad hoc solution from magneto-gas dynamics. Noh and Protter have found the Lagrange formulation to be a convenient vehicle for obtaining "soft" solutions of the equations of gas dynamics. The book notes that developing solutions in two and three dimensions can be achieved by employing Lagrangian coordinates. The book explores approximate methods that use analytical procedures to obtain solutions in the form of functions approximating solutions of nonlinear problems. Approximate methods include integral equations, boundary theory, maximum operation, and equations of elliptic types. The book can serve and benefit mathematicians, students of, and professors of calculus, statistics, or advanced mathematics.

Handbook of Linear Partial Differential Equations for Engineers and Scientists

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 1420035320
Total Pages : 800 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Linear Partial Differential Equations for Engineers and Scientists by : Andrei D. Polyanin

Download or read book Handbook of Linear Partial Differential Equations for Engineers and Scientists written by Andrei D. Polyanin and published by CRC Press. This book was released on 2001-11-28 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and problems in science and engineering. Parabolic, hyperbolic, and elliptic equations with

Handbook of Nonlinear Partial Differential Equations

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 1135440816
Total Pages : 835 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Handbook of Nonlinear Partial Differential Equations by : Andrei D. Polyanin

Download or read book Handbook of Nonlinear Partial Differential Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2004-06-02 with total page 835 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:

Analytical Methods for Solving Nonlinear Partial Differential Equations

Author : Daniel Arrigo
Publisher : Springer Nature
ISBN 13 : 3031170695
Total Pages : 181 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Analytical Methods for Solving Nonlinear Partial Differential Equations by : Daniel Arrigo

Download or read book Analytical Methods for Solving Nonlinear Partial Differential Equations written by Daniel Arrigo and published by Springer Nature. This book was released on 2022-10-28 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, readers are introduced to techniques to obtain exact solutions of NLPDEs. The chapters include the following topics: Nonlinear PDEs are Everywhere; Differential Substitutions; Point and Contact Transformations; First Integrals; and Functional Separability. Readers are guided through these chapters and are provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. This Second Edition includes a new method of generating contact transformations and focuses on a solution method (parametric Legendre transformations) to solve a particular class of two nonlinear PDEs.

Handbook of Exact Solutions to Mathematical Equations

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 9780367507992
Total Pages : 0 pages
Book Rating : 4.5/5 (79 download)

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Book Synopsis Handbook of Exact Solutions to Mathematical Equations by : Andrei D. Polyanin

Download or read book Handbook of Exact Solutions to Mathematical Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2024-08-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This Handbook is a unique reference for scientists and engineers, containing over 3,800 nonlinear partial differential equations with solutions. The book concerns first-, second-, third-, fourth-, and higher-order nonlinear PDEs and systems of coupled PDEs. It discusses parabolic, hyperbolic, and elliptic equations as well as those of mixed and general type. All in all, the handbook contains many more nonlinear equations of mathematical physics and other nonlinear PDEs with their exact solutions, than any other book currently available. Apart from the exact solutions, it also provides various reductions and transformations leading to ordinary differential equations, linear PDEs, or simpler PDEs. A solution is called exact if, when substituted into the differential equation under consideration, it turns the equation into an identity. In this case, no approximations or simplifications of the equation are allowed, and no a priori assumptions are used. Exact solutions to nonlinear equations of mathematical physics are understood as follows: solutions expressed in terms of elementary functions, functions included in the equation (this is necessary when the equation depends on arbitrary functions), and indefinite integrals; solutions expressed in terms of solutions to ordinary differential equations or systems of such equations. Exact solutions of mathematical equations have always played and continue to play a massive role in forming a correct understanding of the qualitative features of many phenomena and processes in various fields of natural science. The book will be helpful for a wide range of researchers, university teachers, and graduate and postgraduate students specializing in the fields of applied and computational mathematics, mathematical and theoretical physics, continuum mechanics, control theory, biology, biophysics, biochemistry, medicine, chemical engineering sciences, and ecology"--

An Introduction to Partial Differential Equations

Author : Daniel J. Arrigo
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681732556
Total Pages : 169 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis An Introduction to Partial Differential Equations by : Daniel J. Arrigo

Download or read book An Introduction to Partial Differential Equations written by Daniel J. Arrigo and published by Morgan & Claypool Publishers. This book was released on 2017-12-18 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to methods for solving partial differential equations (PDEs). After the introduction of the main four PDEs that could be considered the cornerstone of Applied Mathematics, the reader is introduced to a variety of PDEs that come from a variety of fields in the Natural Sciences and Engineering and is a springboard into this wonderful subject. The chapters include the following topics: First-order PDEs, Second-order PDEs, Fourier Series, Separation of Variables, and the Fourier Transform. The reader is guided through these chapters where techniques for solving first- and second-order PDEs are introduced. Each chapter ends with a series of exercises illustrating the material presented in each chapter. The book can be used as a textbook for any introductory course in PDEs typically found in both science and engineering programs and has been used at the University of Central Arkansas for over ten years.

Linear Partial Differential Equations for Scientists and Engineers

Author : Tyn Myint-U
Publisher : Springer Science & Business Media
ISBN 13 : 0817645608
Total Pages : 778 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Linear Partial Differential Equations for Scientists and Engineers by : Tyn Myint-U

Download or read book Linear Partial Differential Equations for Scientists and Engineers written by Tyn Myint-U and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry; solutions are provided.

An Introduction to Partial Differential Equations

Author : Daniel Arrigo
Publisher : Springer Nature
ISBN 13 : 3031220870
Total Pages : 208 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis An Introduction to Partial Differential Equations by : Daniel Arrigo

Download or read book An Introduction to Partial Differential Equations written by Daniel Arrigo and published by Springer Nature. This book was released on 2023-01-20 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to the methods needed to solve partial differential equations (PDEs). Readers are introduced to PDEs that come from a variety of fields in engineering and the natural sciences. The chapters include the following topics: First Order PDEs, Second Order PDEs, Fourier Series, Separation of Variables, the Fourier Transform, and higher dimensional problems. Readers are guided through these chapters where techniques for solving first and second order PDEs are introduced. Each chapter ends with series of exercises to facilitate learning as well as illustrate the material presented in each chapter.

Partial Differential Equations and Solitary Waves Theory

Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
ISBN 13 : 364200251X
Total Pages : 700 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Partial Differential Equations and Solitary Waves Theory by : Abdul-Majid Wazwaz

Download or read book Partial Differential Equations and Solitary Waves Theory written by Abdul-Majid Wazwaz and published by Springer Science & Business Media. This book was released on 2010-05-28 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.

Delay Ordinary and Partial Differential Equations

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 1000925897
Total Pages : 434 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Delay Ordinary and Partial Differential Equations by : Andrei D. Polyanin

Download or read book Delay Ordinary and Partial Differential Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2023-08-28 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides exact solutions Describes numerical methods or numerical solutions, analytical methods, stability/instability issues Focus on partial differential equations

Elementary Differential Equations with Boundary Value Problems

Author : William F. Trench
Publisher : Thomson Brooks/Cole
ISBN 13 :
Total Pages : 766 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Elementary Differential Equations with Boundary Value Problems by : William F. Trench

Download or read book Elementary Differential Equations with Boundary Value Problems written by William F. Trench and published by Thomson Brooks/Cole. This book was released on 2001 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.

Analytical Techniques for Solving Nonlinear Partial Differential Equations

Author : Daniel J. Arrigo
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681735342
Total Pages : 167 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis Analytical Techniques for Solving Nonlinear Partial Differential Equations by : Daniel J. Arrigo

Download or read book Analytical Techniques for Solving Nonlinear Partial Differential Equations written by Daniel J. Arrigo and published by Morgan & Claypool Publishers. This book was released on 2019-06-06 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, the reader is introduced to techniques used to obtain exact solutions of NPDEs. The chapters include the following topics: Compatibility, Differential Substitutions, Point and Contact Transformations, First Integrals, and Functional Separability. The reader is guided through these chapters and is provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. The book can be used as a textbook for a second course in PDEs (typically found in both science and engineering programs) and has been used at the University of Central Arkansas for more than ten years.