Traveling Wave Analysis of Partial Differential Equations

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  • Publisher : Academic Press
  • Release : 09 December 2010
  • ISBN : 0123846536
  • Page : 461 pages
  • Rating : 4.5/5 from 103 voters

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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

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Traveling Wave Analysis of Partial Differential Equations

Traveling Wave Analysis of Partial Differential Equations
  • Author : Graham Griffiths,William E. Schiesser
  • Publisher : Academic Press
  • Release Date : 2010-12-09
  • ISBN : 0123846536
GET THIS BOOKTraveling Wave Analysis of Partial Differential Equations

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

A Compendium of Partial Differential Equation Models

A Compendium of Partial Differential Equation Models
  • Author : William E. Schiesser,Graham W. Griffiths
  • Publisher : Cambridge University Press
  • Release Date : 2009-03-16
  • ISBN : 9780521519861
GET THIS BOOKA Compendium of Partial Differential Equation Models

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

Partial Differential Equations

Partial Differential Equations
  • Author : Walter A. Strauss
  • Publisher : John Wiley & Sons
  • Release Date : 2007-12-21
  • ISBN : 9780470054567
GET THIS BOOKPartial Differential Equations

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

Partial Differential Equations

Partial Differential Equations
  • Author : Michael Shearer,Rachel Levy
  • Publisher : Princeton University Press
  • Release Date : 2015-03-01
  • ISBN : 9781400866601
GET THIS BOOKPartial Differential Equations

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

Partial Differential Equations and Solitary Waves Theory

Partial Differential Equations and Solitary Waves Theory
  • Author : Abdul-Majid Wazwaz
  • Publisher : Springer Science & Business Media
  • Release Date : 2010-05-28
  • ISBN : 9783642002519
GET THIS BOOKPartial Differential Equations and Solitary Waves Theory

"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

Traveling Wave Analysis of Partial Differential Equations

Traveling Wave Analysis of Partial Differential Equations
  • Author : Graham W. Griffiths,W. E. Schiesser
  • Publisher : Unknown
  • Release Date : 2011-01
  • ISBN : 0123846528
GET THIS BOOKTraveling Wave Analysis of Partial Differential Equations

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

A First Course in Partial Differential Equations

A First Course in Partial Differential Equations
  • Author : J Robert Buchanan,Zhoude Shao
  • Publisher : World Scientific Publishing Company
  • Release Date : 2017-10-30
  • ISBN : 9789813226456
GET THIS BOOKA First Course in Partial Differential Equations

Resources for instructors who adopt this textbook:Lecture SlidesInstructors' Manual (complete solutions and supporting work)Students' Manual (final answers to computational exercises) Kindly send your requests to [email protected] This textbook gives an introduction to Partial Differential Equations (PDEs), for any reader wishing to learn and understand the basic concepts, theory, and solution techniques of elementary PDEs. The only prerequisite is an undergraduate course in Ordinary Differential Equations. This work contains a comprehensive treatment of the standard second-order linear

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  • Author : Sergei Silvestrov,Milica Rančić
  • Publisher : Springer
  • Release Date : 2017-02-10
  • ISBN : 9783319421056
GET THIS BOOKEngineering Mathematics II

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and

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  • Author : Robert A. Meyers
  • Publisher : Springer Science & Business Media
  • Release Date : 2011-10-05
  • ISBN : 9781461418054
GET THIS BOOKMathematics of Complexity and Dynamical Systems

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior

Solitons, Nonlinear Evolution Equations and Inverse Scattering

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  • Author : Mark J. Ablowitz,M. A. Ablowitz,P. A. Clarkson
  • Publisher : Cambridge University Press
  • Release Date : 1991-12-12
  • ISBN : 9780521387309
GET THIS BOOKSolitons, Nonlinear Evolution Equations and Inverse Scattering

This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

Self-Similarity and Beyond

Self-Similarity and Beyond
  • Author : P.L. Sachdev
  • Publisher : CRC Press
  • Release Date : 2019-06-13
  • ISBN : 9781000611410
GET THIS BOOKSelf-Similarity and Beyond

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

Linear Partial Differential Equations and Fourier Theory

Linear Partial Differential Equations and Fourier Theory
  • Author : Marcus Pivato
  • Publisher : Cambridge University Press
  • Release Date : 2010-01-07
  • ISBN : 9780521199704
GET THIS BOOKLinear Partial Differential Equations and Fourier Theory

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

Proceedings of International Conference on Trends in Computational and Cognitive Engineering

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  • Author : Phool Singh,Rajesh Kumar Gupta,Kanad Ray,Anirban Bandyopadhyay
  • Publisher : Springer Nature
  • Release Date : 2020-09-30
  • ISBN : 9789811554148
GET THIS BOOKProceedings of International Conference on Trends in Computational and Cognitive Engineering

This book presents various computational and cognitive modeling approaches in the areas of health, education, finance, theenvironment, engineering, commerce and industry. Gathering selected conference papers presented atthe International Conference on Trends in Computational and Cognitive Engineering (TCCE), it sharescutting-edge insights and ideas from mathematicians, engineers, scientists and researchers anddiscusses fresh perspectives on problem solving in a range of research areas.

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations
  • Author : Hans G. Kaper,Marc Garbey
  • Publisher : CRC Press
  • Release Date : 1991-02-25
  • ISBN : 0585319677
GET THIS BOOKAsymptotic Analysis and the Numerical Solution of Partial Differential Equations

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

Theory and Applications of Partial Functional Differential Equations

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  • Author : Jianhong Wu
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • ISBN : 9781461240501
GET THIS BOOKTheory and Applications of Partial Functional Differential Equations

Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in