Traveling Wave Analysis of Partial Differential Equations
  • Author : Graham Griffiths
  • Release Date : 09 December 2010
  • Publisher : Academic Press
  • Genre : Mathematics
  • Pages : 461
  • ISBN 13 : 0123846536

Traveling Wave Analysis of Partial Differential Equations Book Summary

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 : Graham Griffiths,William E. Schiesser
Publisher : Academic Press
Genre : Mathematics
Total View : 5639 Views
File Size : 41,7 Mb
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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 ...

Traveling Wave Analysis of Partial Differential Equations

Traveling Wave Analysis of Partial Differential Equations

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Publisher : Unknown
Genre : Computers
Total View : 3544 Views
File Size : 40,5 Mb
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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 ...

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Publisher : American Mathematical Soc.
Genre : Mathematics
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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 ...

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Publisher : John Wiley & Sons
Genre : Mathematics
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Publisher : Princeton University Press
Genre : Mathematics
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Traveling Wave Solutions of Parabolic Systems

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Author : A. I. Volpert,Vitaly A. Volpert,Vladimir A. Volpert
Publisher : American Mathematical Soc.
Genre : Mathematics
Total View : 9050 Views
File Size : 41,8 Mb
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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 ...