Traveling Wave Analysis of Partial Differential Equations

Traveling Wave Analysis of Partial Differential Equations

Numerical and Analytical Methods with Matlab and Maple

1st Edition - December 9, 2010

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  • Authors: Graham Griffiths, William Schiesser
  • eBook ISBN: 9780123846532
  • Hardcover ISBN: 9780123846525

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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.

Key Features

  • 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


Scientists, Engineers, Applied Mathematicians, and Economists who use PDE models

Table of Contents

  • Dedication


    1. Introduction to Traveling Wave Analysis

    2. Linear Advection Equation

    3. Linear Diffusion Equation

    4. A Linear Convection Diffusion Reaction Equation

    5. Diffusion Equation with Onlinear Source Terms

    6. Burgers–Huxley Equation

    7. Burgers–Fisher Equation

    8. Fisher–Kolmogorov Equation

    9. Fitzhugh–Nagumo Equation

    10. Kolmogorov–Petrovskii–Piskunov Equation

    11. Kuramoto–Sivashinsky Equation

    12. Kawahara Equation

    13. Regularized Long-Wave Equation

    14. Extended Bernoulli Equation

    15. Hyperbolic Liouville Equation

    16. Sine-Gordon Equation

    17. Mth-Order Klein–Gordon Equation

    18. Boussinesq Equation

    19. Modified Wave Equation

    A. Analytical Solution Methods for Traveling Wave Problems


Product details

  • No. of pages: 461
  • Language: English
  • Copyright: © Academic Press 2011
  • Published: December 9, 2010
  • Imprint: Academic Press
  • eBook ISBN: 9780123846532
  • Hardcover ISBN: 9780123846525

About the Authors

Graham Griffiths

William Schiesser

The R routines are available from Queries about the routines can be directed to W.E. Schiesser is Emeritus McCann Professor of Chemical and Biomolecular Engineering and Professor of Mathematics at Lehigh University. He holds a PhD from Princeton University and a ScD (hon) from the University of Mons, Belgium. His research is directed toward numerical methods and associated software for ordinary, differential-algebraic and partial differential equations (ODE/DAE/PDEs), and the development of mathematical models based on ODE/DAE/PDEs. He is the author or coauthor of more than 14 books, and his ODE/DAE/PDE computer routines have been accessed by some 5,000 colleges and universities, corporations and government agencies.

Affiliations and Expertise

Lehigh University

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