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Traveling Wave Analysis Of Partial Differential Equations

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Traveling Wave Analysis of Partial Differential Equations

Traveling Wave Analysis of Partial Differential Equations Book
Author : Graham W. Griffiths,W. E. Schiesser
Publisher : Unknown
Release : 2011-01
ISBN : 9780123846525
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : William E. Schiesser,Graham W. Griffiths
Publisher : Unknown
Release : 2011
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Traveling Wave Analysis of Partial Differential Equations book written by William E. Schiesser,Graham W. Griffiths, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Traveling Wave Analysis of Partial Differential Equations

Traveling Wave Analysis of Partial Differential Equations Book
Author : Graham Griffiths,William E. Schiesser
Publisher : Academic Press
Release : 2010-12-09
ISBN : 9780123846532
Language : En, Es, Fr & De

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Book Description :

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

Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena

Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena Book
Author : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
Publisher : American Mathematical Soc.
Release : 2010-10-01
ISBN : 082184976X
Language : En, Es, Fr & De

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Book Description :

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.

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations Book
Author : Hans G. Kaper,Marc Garbey
Publisher : CRC Press
Release : 1991-02-25
ISBN : 9780585319674
Language : En, Es, Fr & De

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Book Description :

Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per

Partial Differential Equations

Partial Differential Equations Book
Author : Michael Shearer,Rachel Levy
Publisher : Princeton University Press
Release : 2015-03-01
ISBN : 0691161291
Language : En, Es, Fr & De

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Book Description :

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

Mathematical Methods in Engineering

Mathematical Methods in Engineering Book
Author : Kenan Taş,Dumitru Baleanu,J. A. Tenreiro Machado
Publisher : Springer
Release : 2018-08-02
ISBN : 331990972X
Language : En, Es, Fr & De

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Book Description :

This book presents recent developments in nonlinear dynamics with an emphasis on complex systems. The volume illustrates new methods to characterize the solutions of nonlinear dynamics associated with complex systems. This book contains the following topics: new solutions of the functional equations, optimization algorithm for traveling salesman problem, fractals, control, fractional calculus models, fractional discretization, local fractional partial differential equations and their applications, and solutions of fractional kinetic equations.

Recent Trends in Wave Mechanics and Vibrations

Recent Trends in Wave Mechanics and Vibrations Book
Author : S. Chakraverty,Paritosh Biswas
Publisher : Springer Nature
Release : 2019-11-12
ISBN : 9811502870
Language : En, Es, Fr & De

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Book Description :

This book consists of select proceedings of the National Conference on Wave Mechanics and Vibrations (WMVC 2018). It covers recent developments and cutting-edge methods in wave mechanics and vibrations applied to a wide range of engineering problems. The book presents analytical and computational studies in structural mechanics, seismology and earthquake engineering, mechanical engineering, aeronautics, robotics and nuclear engineering among others. This book can be useful for students, researchers, and professionals interested in the wide-ranging applications of wave mechanics and vibrations.

Spline Collocation Methods for Partial Differential Equations

Spline Collocation Methods for Partial Differential Equations Book
Author : William E. Schiesser
Publisher : John Wiley & Sons
Release : 2017-05-22
ISBN : 1119301033
Language : En, Es, Fr & De

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Book Description :

One-dimensional PDEs -- Multidimensional PDEs -- Navier-Stokes, Burgers equations -- Korteweg-deVries equation -- Maxwell equations -- Poisson-Nernst-Planck equations -- Fokker-Planck equation -- Fisher-Kolmogorov equation -- Klein-Gordon equation -- Boussinesq equation -- Cahn-Hilliard equation -- Camassa-Holm equation -- Burgers-Huxley equation -- Gierer-Meinhardt equations -- Keller-Segel equations -- Fitzhugh-Nagumo equations -- Euler-Poisson-Darboux equation -- Kuramoto-Sivashinsky equation -- Einstein-Maxwell equations

Partial Differential Equation Analysis in Biomedical Engineering

Partial Differential Equation Analysis in Biomedical Engineering Book
Author : W. E. Schiesser
Publisher : Cambridge University Press
Release : 2012-11-15
ISBN : 1107022800
Language : En, Es, Fr & De

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Book Description :

Gives graduate students and researchers an introductory overview of partial differential equation analysis of biomedical engineering systems through detailed examples.

Handbook of Nonlinear Partial Differential Equations Second Edition

Handbook of Nonlinear Partial Differential Equations  Second Edition Book
Author : Andrei D. Polyanin,Valentin F. Zaitsev
Publisher : CRC Press
Release : 2016-04-19
ISBN : 142008724X
Language : En, Es, Fr & De

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Book Description :

New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with MapleTM, Mathematica®, and MATLAB® Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They outline the methods in a schematic, simplified manner and arrange the material in increasing order of complexity.

Numerical Integration of Space Fractional Partial Differential Equations

Numerical Integration of Space Fractional Partial Differential Equations Book
Author : Younes Salehi,William E. Schiesser
Publisher : Morgan & Claypool Publishers
Release : 2017-12-06
ISBN : 1681732106
Language : En, Es, Fr & De

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Book Description :

Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: •Vol 1: Introduction to Algorithms and Computer Coding in R •Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. In the second volume, the emphasis is on applications of SFPDEs developed mainly through the extension of classical integer PDEs to SFPDEs. The example applications are: •Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions •Fisher-Kolmogorov SFPDE •Burgers SFPDE •Fokker-Planck SFPDE •Burgers-Huxley SFPDE •Fitzhugh-Nagumo SFPDE. These SFPDEs were selected because they are integer first order in time and integer second order in space. The variation in the spatial derivative from order two (parabolic) to order one (first order hyperbolic) demonstrates the effect of the spatial fractional order ?? with 1 ≤ ?? ≤ 2. All of the example SFPDEs are one dimensional in Cartesian coordinates. Extensions to higher dimensions and other coordinate systems, in principle, follow from the examples in this second volume. The examples start with a statement of the integer PDEs that are then extended to SFPDEs. The format of each chapter is the same as in the first volume. The R routines can be downloaded and executed on a modest computer (R is readily available from the Internet).

Differential Equation Analysis in Biomedical Science and Engineering

Differential Equation Analysis in Biomedical Science and Engineering Book
Author : William E. Schiesser
Publisher : John Wiley & Sons
Release : 2014-03-31
ISBN : 1118705165
Language : En, Es, Fr & De

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Book Description :

Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear partial differential equations. The author’s primary focus is on models expressed as systems of PDEs, which generally result from including spatial effects so that the PDE dependent variables are functions of both space and time, unlike ordinary differential equation (ODE) systems that pertain to time only. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for PDEs Models as systems of PDEs and associated initial and boundary conditions with explanations of the associated chemistry, physics, biology, and physiology Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general PDE computation through various biomedical science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.

Elliptic Partial Differential Equations

Elliptic Partial Differential Equations Book
Author : Vitaly Volpert
Publisher : Springer
Release : 2014-05-10
ISBN : 3034808135
Language : En, Es, Fr & De

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Book Description :

If we had to formulate in one sentence what this book is about, it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered.

Topics in Modal Analysis II Volume 6

Topics in Modal Analysis II  Volume 6 Book
Author : R. Allemang,J. De Clerck,C. Niezrecki,J.R. Blough
Publisher : Springer Science & Business Media
Release : 2012-04-28
ISBN : 1461424194
Language : En, Es, Fr & De

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Book Description :

Topics in Modal Analysis II, Volume 6: Proceedings of the 30th IMAC, A Conference and Exposition on Structural Dynamics, 2012, is the sixth volume of six from the Conference and brings together 65 contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Aerospace, Acoustics, Energy Harvesting, Shock and Vibration, Finite Element, Structural Health Monitoring, Biodynamics Experimental Techniques, Damage Detection, Rotating Machinery, Sports Equipment Dynamics, Aircraft/Aerospace.

Method of Lines PDE Analysis in Biomedical Science and Engineering

Method of Lines PDE Analysis in Biomedical Science and Engineering Book
Author : William E. Schiesser
Publisher : John Wiley & Sons
Release : 2016-04-13
ISBN : 1119130514
Language : En, Es, Fr & De

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Book Description :

Presents the methodology and applications of ODE and PDE models within biomedical science and engineering With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineering demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Written by a well-known researcher in the field, the book provides an introduction to basic numerical methods for initial/boundary value PDEs before moving on to specific BMSE applications of PDEs. Featuring a straightforward approach, the book’s chapters follow a consistent and comprehensive format. First, each chapter begins by presenting the model as an ordinary differential equation (ODE)/PDE system, including the initial and boundary conditions. Next, the programming of the model equations is introduced through a series of R routines that primarily implement MOL for PDEs. Subsequently, the resulting numerical and graphical solution is discussed and interpreted with respect to the model equations. Finally, each chapter concludes with a review of the numerical algorithm performance, general observations and results, and possible extensions of the model. Method of Lines PDE Analysis in Biomedical Science and Engineering also includes: Examples of MOL analysis of PDEs, including BMSE applications in wave front resolution in chromatography, VEGF angiogenesis, thermographic tumor location, blood-tissue transport, two fluid and membrane mass transfer, artificial liver support system, cross diffusion epidemiology, oncolytic virotherapy, tumor cell density in glioblastomas, and variable grids Discussions on the use of R software, which facilitates immediate solutions to differential equation problems without having to first learn the basic concepts of numerical analysis for PDEs and the programming of PDE algorithms A companion website that provides source code for the R routines Method of Lines PDE Analysis in Biomedical Science and Engineering is an introductory reference for researchers, scientists, clinicians, medical researchers, mathematicians, statisticians, chemical engineers, epidemiologists, and pharmacokineticists as well as anyone interested in clinical applications and the interpretation of experimental data with differential equation models. The book is also an ideal textbook for graduate-level courses in applied mathematics, BMSE, biology, biophysics, biochemistry, medicine, and engineering.

Geometric Analysis of Nonlinear Partial Differential Equations

Geometric Analysis of Nonlinear Partial Differential Equations Book
Author : Valentin Lychagin,Joseph Krasilshchik
Publisher : MDPI
Release : 2021-09-03
ISBN : 303651046X
Language : En, Es, Fr & De

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Book Description :

This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.

Solving Differential Equations in R

Solving Differential Equations in R Book
Author : Karline Soetaert,Jeff Cash,Francesca Mazzia
Publisher : Springer Science & Business Media
Release : 2012-06-06
ISBN : 3642280706
Language : En, Es, Fr & De

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Book Description :

Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.

Separation of Variables and Exact Solutions to Nonlinear PDEs

Separation of Variables and Exact Solutions to Nonlinear PDEs Book
Author : Andrei D. Polyanin,Alexei I. Zhurov
Publisher : CRC Press
Release : 2021-09-20
ISBN : 100046363X
Language : En, Es, Fr & De

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Book Description :

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.

U S Government Research Reports

U S  Government Research Reports Book
Author : Anonim
Publisher : Unknown
Release : 1962
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download U S Government Research Reports book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.