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Traveling Wave Analysis of Partial Differential Equations
 
 

Traveling Wave Analysis of Partial Differential Equations, 1st Edition

Numerical and Analytical Methods with Matlab and Maple

 
Traveling Wave Analysis of Partial Differential Equations, 1st Edition,Graham Griffiths,William Schiesser,ISBN9780123846525
 
 
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Academic Press

9780123846525

9780123846532

464

240 X 197

Surveys new developments in analytical and numerical methods, and relates the two through a series of partial differential equations examples

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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

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

Readership

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

Information about this author is currently not available.

William Schiesser

Affiliations and Expertise

Lehigh University

View additional works by William E. Schiesser

Traveling Wave Analysis of Partial Differential Equations, 1st Edition

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

Quotes and 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

 
 
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