Traveling Wave Analysis Of Partial Differential Equations
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Traveling Wave Analysis Of Partial Differential Equations
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Author : William E. Schiesser
language : en
Publisher:
Release Date : 2011
Traveling Wave Analysis Of Partial Differential Equations written by William E. Schiesser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Differential equations, Partial categories.
Traveling Wave Analysis Of Partial Differential Equations
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Author : Graham Griffiths
language : en
Publisher: Academic Press
Release Date : 2010-12-09
Traveling Wave Analysis Of Partial Differential Equations written by Graham Griffiths and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-09 with Mathematics categories.
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
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Author : Graham W. Griffiths
language : en
Publisher:
Release Date : 2011-01
Traveling Wave Analysis Of Partial Differential Equations written by Graham W. Griffiths and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01 with Computers categories.
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.
Partial Differential Equations
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Author : Michael Shearer
language : en
Publisher: Princeton University Press
Release Date : 2015-03-01
Partial Differential Equations written by Michael Shearer and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-01 with Mathematics categories.
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
An Introduction To Nonlinear Partial Differential Equations
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Author : J. David Logan
language : en
Publisher: John Wiley & Sons
Release Date : 2008-04-11
An Introduction To Nonlinear Partial Differential Equations written by J. David Logan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-11 with Mathematics categories.
Praise for the First Edition: "This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds." —SIAM Review A practical introduction to nonlinear PDEs and their real-world applications Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems. The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include: Additional intermediate-level exercises that facilitate the development of advanced problem-solving skills New applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseases An expanded bibliography that facilitates further investigation into specialized topics With individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.
Nonlinear Partial Differential Equations And Hyperbolic Wave Phenomena
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Author : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-10-01
Nonlinear Partial Differential Equations And Hyperbolic Wave Phenomena written by Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-01 with Mathematics categories.
This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.
Introduction To Qualitative Methods For Differential Equations
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Author : Ronald E. Mickens
language : en
Publisher: CRC Press
Release Date : 2025-05-01
Introduction To Qualitative Methods For Differential Equations written by Ronald E. Mickens and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-01 with Mathematics categories.
Introduction to Qualitative Methods for Differential Equations provides an alternative approach to teaching and understanding differential equations. The basic methodology of the book is centred on finding reformulations of differential equations in such a manner that they become (partially, at least) problems in geometry. Through this approach, the book distils the critical aspects of the qualitative theory of differential equations and illustrates their application to a number of nontrivial problems. Features Self-contained with suggestions for further reading Concise and approachable exposition with only minimal pre-requisites Ideal for self-study Appropriate for undergraduate mathematicians, engineers, and other quantitative science students.
Spline Collocation Methods For Partial Differential Equations
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Author : William E. Schiesser
language : en
Publisher: John Wiley & Sons
Release Date : 2017-05-08
Spline Collocation Methods For Partial Differential Equations written by William E. Schiesser and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-08 with Mathematics categories.
A comprehensive approach to numerical partial differential equations Spline Collocation Methods for Partial Differential Equations combines the collocation analysis of partial differential equations (PDEs) with the method of lines (MOL) in order to simplify the solution process. Using a series of example applications, the author delineates the main features of the approach in detail, including an established mathematical framework. The book also clearly demonstrates that spline collocation can offer a comprehensive method for numerical integration of PDEs when it is used with the MOL in which spatial (boundary value) derivatives are approximated with splines, including the boundary conditions. R, an open-source scientific programming system, is used throughout for programming the PDEs and numerical algorithms, and each section of code is clearly explained. As a result, readers gain a complete picture of the model and its computer implementation without having to fill in the details of the numerical analysis, algorithms, or programming. The presentation is not heavily mathematical, and in place of theorems and proofs, detailed example applications are provided. Appropriate for scientists, engineers, and applied mathematicians, Spline Collocation Methods for Partial Differential Equations: Introduces numerical methods by first presenting basic examples followed by more complicated applications Employs R to illustrate accurate and efficient solutions of the PDE models Presents spline collocation as a comprehensive approach to the numerical integration of PDEs and an effective alternative to other, well established methods Discusses how to reproduce and extend the presented numerical solutions Identifies the use of selected algorithms, such as the solution of nonlinear equations and banded or sparse matrix processing Features a companion website that provides the related R routines Spline Collocation Methods for Partial Differential Equations is a valuable reference and/or self-study guide for academics, researchers, and practitioners in applied mathematics and engineering, as well as for advanced undergraduates and graduate-level students.
U S Government Research Reports
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Author :
language : en
Publisher:
Release Date : 1962
U S Government Research Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Research categories.
Traveling Wave Solutions Of Parabolic Systems
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Author : A. I. Volpert
language : en
Publisher: American Mathematical Soc.
Release Date :
Traveling Wave Solutions Of Parabolic Systems written by A. I. Volpert and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.