Traveling Wave Analysis of Partial Differential Equations

Traveling Wave Analysis of Partial Differential Equations
Author: Graham W. Griffiths,W. E. Schiesser
Publsiher: Unknown
Total Pages: 447
Release: 2011-01
ISBN 10: 9780123846525
ISBN 13: 0123846528
Language: EN, FR, DE, ES & NL

Traveling Wave Analysis of Partial Differential Equations Book Review:

Partial Differential Equations have been developed and used in science and engineering for more than 200 years, yet they remain a very active area of research, both because of their role in mathematics and their application to virtually all areas of science and engineering. This research is due relatively recently to the development of computer solution methods for PDEs that have extended PDE applications in quantifying board areas of physical, chemical, and biological phenomena. This book surveys some of these new development in analytical and numerical method, and relates the two through a series of PDF examples. The PDFs that have been selected are largely, "named" in thee sense that they have the names of their original contributors. These names usually reflect that the PDFs are widely recognized and used in many application areas. The development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problem that can be used to evaluate numerical methods.

Traveling Wave Analysis of Partial Differential Equations

Traveling Wave Analysis of Partial Differential Equations
Author: Graham Griffiths,William E. Schiesser
Publsiher: Academic Press
Total Pages: 461
Release: 2010-12-09
ISBN 10: 9780123846532
ISBN 13: 0123846536
Language: EN, FR, DE, ES & NL

Traveling Wave Analysis of Partial Differential Equations Book Review:

Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors’ intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs. The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net Includes a spectrum of applications in science, engineering, applied mathematics Presents a combination of numerical and analytical methods Provides transportable computer codes in Matlab and Maple

Traveling Wave Analysis of Partial Differential Equations

Traveling Wave Analysis of Partial Differential Equations
Author: William E. Schiesser,Graham W. Griffiths
Publsiher: Unknown
Total Pages: 447
Release: 2011
ISBN 10:
ISBN 13: OCLC:733447329
Language: EN, FR, DE, ES & NL

Traveling Wave Analysis of Partial Differential Equations Book Review:

A Compendium of Partial Differential Equation Models

A Compendium of Partial Differential Equation Models
Author: William E. Schiesser,Graham W. Griffiths
Publsiher: Cambridge University Press
Total Pages: 474
Release: 2009-03-16
ISBN 10: 0521519861
ISBN 13: 9780521519861
Language: EN, FR, DE, ES & NL

A Compendium of Partial Differential Equation Models Book Review:

Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.

Partial Differential Equations and Solitary Waves Theory

Partial Differential Equations and Solitary Waves Theory
Author: Abdul-Majid Wazwaz
Publsiher: Springer Science & Business Media
Total Pages: 700
Release: 2010-05-28
ISBN 10: 364200251X
ISBN 13: 9783642002519
Language: EN, FR, DE, ES & NL

Partial Differential Equations and Solitary Waves Theory Book Review:

"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.

Traveling Wave Solutions of Parabolic Systems

Traveling Wave Solutions of Parabolic Systems
Author: A. I. Volpert,Vitaly A. Volpert,Vladimir A. Volpert
Publsiher: American Mathematical Soc.
Total Pages: 448
Release: 2021
ISBN 10: 9780821897577
ISBN 13: 0821897578
Language: EN, FR, DE, ES & NL

Traveling Wave Solutions of Parabolic Systems Book Review:

The theory of travelling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. With introductory material accessible to non-mathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.

An Introduction to the Mathematical Theory of Waves

An Introduction to the Mathematical Theory of Waves
Author: Roger Knobel
Publsiher: American Mathematical Soc.
Total Pages: 196
Release: 2000
ISBN 10: 0821820397
ISBN 13: 9780821820391
Language: EN, FR, DE, ES & NL

An Introduction to the Mathematical Theory of Waves Book Review:

Linear and nonlinear waves are a central part of the theory of PDEs. This book begins with a description of one-dimensional waves and their visualization through computer-aided techniques. Next, traveling waves are covered, such as solitary waves for the Klein-Gordon and KdV equations. Finally, the author gives a lucid discussion of waves arising from conservation laws, including shock and rarefaction waves. As an application, interesting models of traffic flow are used to illustrate conservation laws and wave phenomena. This book is based on a course given by the author at the IAS/Park City Mathematics Institute. It is suitable for independent study by undergraduate students in mathematics, engineering, and science programs. This book is published in cooperation with IAS/Park City Mathematics Institute.

Solving Frontier Problems of Physics The Decomposition Method

Solving Frontier Problems of Physics  The Decomposition Method
Author: G. Adomian
Publsiher: Springer Science & Business Media
Total Pages: 354
Release: 2013-06-29
ISBN 10: 9401582890
ISBN 13: 9789401582896
Language: EN, FR, DE, ES & NL

Solving Frontier Problems of Physics The Decomposition Method Book Review:

The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations.

Partial Differential Equations

Partial Differential Equations
Author: Michael Shearer,Rachel Levy
Publsiher: Princeton University Press
Total Pages: 288
Release: 2015-03-01
ISBN 10: 140086660X
ISBN 13: 9781400866601
Language: EN, FR, DE, ES & NL

Partial Differential Equations Book Review:

An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors

Nonlinear Systems of Partial Differential Equations

Nonlinear Systems of Partial Differential Equations
Author: Anonim
Publsiher: Unknown
Total Pages: 329
Release: 2021
ISBN 10: 9814467472
ISBN 13: 9789814467476
Language: EN, FR, DE, ES & NL

Nonlinear Systems of Partial Differential Equations Book Review:

Partial Differential Equations

Partial Differential Equations
Author: Michael Shearer,Rachel Levy
Publsiher: Princeton University Press
Total Pages: 288
Release: 2015-03-01
ISBN 10: 0691161291
ISBN 13: 9780691161297
Language: EN, FR, DE, ES & NL

Partial Differential Equations Book Review:

An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors

Numerical Analysis Using R

Numerical Analysis Using R
Author: Graham W. Griffiths
Publsiher: Cambridge University Press
Total Pages: 500
Release: 2016-04-22
ISBN 10: 1107115612
ISBN 13: 9781107115613
Language: EN, FR, DE, ES & NL

Numerical Analysis Using R Book Review:

This book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language R, allowing integration with more statistically based methods. The book begins with standard techniques, followed by an overview of 'high resolution' flux limiters and WENO to solve problems with solutions exhibiting high gradient phenomena. Meshless methods using radial basis functions are then discussed in the context of scattered data interpolation and the solution of PDEs on irregular grids. Three detailed case studies demonstrate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book will be useful to students and practitioners in all areas of science and engineering, especially those using R.

Introduction to Partial Differential Equations

Introduction to Partial Differential Equations
Author: Peter J. Olver
Publsiher: Springer Science & Business Media
Total Pages: 636
Release: 2013-11-08
ISBN 10: 3319020994
ISBN 13: 9783319020990
Language: EN, FR, DE, ES & NL

Introduction to Partial Differential Equations Book Review:

This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.

Applied Partial Differential Equations

Applied Partial Differential Equations
Author: J. David Logan
Publsiher: Springer Science & Business Media
Total Pages: 181
Release: 2012-12-06
ISBN 10: 1468405330
ISBN 13: 9781468405330
Language: EN, FR, DE, ES & NL

Applied Partial Differential Equations Book Review:

This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems;' The audience usually consists of stu dents in mathematics, engineering, and the physical sciences. The topics include derivations of some of the standard equations of mathemati cal physics (including the heat equation, the· wave equation, and the Laplace's equation) and methods for solving those equations on bounded and unbounded domains. Methods include eigenfunction expansions or separation of variables, and methods based on Fourier and Laplace transforms. Prerequisites include calculus and a post-calculus differential equations course. There are several excellent texts for this course, so one can legitimately ask why one would wish to write another. A survey of the content of the existing titles shows that their scope is broad and the analysis detailed; and they often exceed five hundred pages in length. These books gen erally have enough material for two, three, or even four semesters. Yet, many undergraduate courses are one-semester courses. The author has often felt that students become a little uncomfortable when an instructor jumps around in a long volume searching for the right topics, or only par tially covers some topics; but they are secure in completely mastering a short, well-defined introduction. This text was written to proVide a brief, one-semester introduction to partial differential equations.

Partial Differential Equations

Partial Differential Equations
Author: Walter A. Strauss
Publsiher: John Wiley & Sons
Total Pages: 464
Release: 2007-12-21
ISBN 10: 0470054565
ISBN 13: 9780470054567
Language: EN, FR, DE, ES & NL

Partial Differential Equations Book Review:

Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables. While focusing on the three most classical partial differential equations (PDEs)—the wave, heat, and Laplace equations—this detailed text also presents a broad practical perspective that merges mathematical concepts with real-world application in diverse areas including molecular structure, photon and electron interactions, radiation of electromagnetic waves, vibrations of a solid, and many more. Rigorous pedagogical tools aid in student comprehension; advanced topics are introduced frequently, with minimal technical jargon, and a wealth of exercises reinforce vital skills and invite additional self-study. Topics are presented in a logical progression, with major concepts such as wave propagation, heat and diffusion, electrostatics, and quantum mechanics placed in contexts familiar to students of various fields in science and engineering. By understanding the properties and applications of PDEs, students will be equipped to better analyze and interpret central processes of the natural world.

Self Similarity and Beyond

Self Similarity and Beyond
Author: P.L. Sachdev
Publsiher: CRC Press
Total Pages: 336
Release: 2019-06-13
ISBN 10: 1000611418
ISBN 13: 9781000611410
Language: EN, FR, DE, ES & NL

Self Similarity and Beyond Book Review:

Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out. Self-Similarity and Beyond presents

Solitons Nonlinear Evolution Equations and Inverse Scattering

Solitons  Nonlinear Evolution Equations and Inverse Scattering
Author: Mark J. Ablowitz,M. A. Ablowitz,P. A. Clarkson,Peter A.. Clarkson
Publsiher: Cambridge University Press
Total Pages: 516
Release: 1991-12-12
ISBN 10: 9780521387309
ISBN 13: 0521387302
Language: EN, FR, DE, ES & NL

Solitons Nonlinear Evolution Equations and Inverse Scattering Book Review:

This book brings together several aspects of soliton theory currently available only in research papers. Emphasis is given to the multi-dimensional problems which arise and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the dbar method.

Nonlinear Dispersive Waves

Nonlinear Dispersive Waves
Author: Mark J. Ablowitz
Publsiher: Cambridge University Press
Total Pages: 329
Release: 2011-09-08
ISBN 10: 1139503480
ISBN 13: 9781139503488
Language: EN, FR, DE, ES & NL

Nonlinear Dispersive Waves Book Review:

The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.

Linear Partial Differential Equations and Fourier Theory

Linear Partial Differential Equations and Fourier Theory
Author: Marcus Pivato
Publsiher: Cambridge University Press
Total Pages: 601
Release: 2010-01-07
ISBN 10: 0521199700
ISBN 13: 9780521199704
Language: EN, FR, DE, ES & NL

Linear Partial Differential Equations and Fourier Theory Book Review:

This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation.

Reaction diffusion Waves

Reaction diffusion Waves
Author: Arnaud Ducrot,Martine Marion,Vitaly Volpert
Publsiher: Editions Publibook
Total Pages: 113
Release: 2009
ISBN 10: 2748346319
ISBN 13: 9782748346312
Language: EN, FR, DE, ES & NL

Reaction diffusion Waves Book Review: