Traveling Wave Analysis of Partial Differential Equations - 1st Edition - ISBN: 9780123846525, 9780123846532

Traveling Wave Analysis of Partial Differential Equations

1st Edition

Numerical and Analytical Methods with Matlab and Maple

Authors: Graham Griffiths William Schiesser
eBook ISBN: 9780123846532
Hardcover ISBN: 9780123846525
Imprint: Academic Press
Published Date: 6th January 2011
Page Count: 461
Tax/VAT will be calculated at check-out Price includes VAT (GST)
56.95
48.99
78.95
Unavailable
Price includes VAT (GST)
× Read this ebook on your PC, Mac, Apple iOS and Andriod mobile devices and eReader

This ebook is protected by Adobe Content Server digital rights management.

For more information on how to use .acsm files please click the Ebook Format Help link.

Institutional Access

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.

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

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

Readership

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

Table of Contents

Dedication

Preface

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

Index

Details

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

About the Author

Graham Griffiths

William Schiesser

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

Reviews

"This book surveys some of the new developments in analytical and numerical computer solution methods for partial differential equations with applications to physical, chemical, and biological problems. The 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."--Zentralblatt MATH 1228-1