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Solving Nonlinear Partial Differential Equations with Maple and Mathematica

  • Book
  • © 2011

Overview

Authors:
  1. Inna Shingareva

    1. , Dept. of Mathematics, University of Sonora, Sonora, Mexico

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    You can also search for this author in PubMed   Google Scholar

  2. Carlos Lizárraga-Celaya

    1. , Departamento de Física, Universidad de Sonora, Sonora, Mexico

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Presents different approaches for solving nonlinear PDEs and systems.
  • Contains numerous examples and comparisons.
  • Use of two computer algebra systems, Maple and Mathematica, enables comparisons between various types of solutions and approaches.
  • Compact and understandable programming style of Maple and Mathematica helps to understand and solve nonlinear PDEs and many other differential equations
  • Includes supplementary material: sn.pub/extras

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Inna Shingareva, Carlos Lizárraga-Celaya
    Pages 1-34

  3. Algebraic Approach

    • Inna Shingareva, Carlos Lizárraga-Celaya
    Pages 35-144

  4. Geometric-Qualitative Approach

    • Inna Shingareva, Carlos Lizárraga-Celaya
    Pages 145-186

  5. General Analytical Approach. Integrability

    • Inna Shingareva, Carlos Lizárraga-Celaya
    Pages 187-226

  6. Approximate Analytical Approach

    • Inna Shingareva, Carlos Lizárraga-Celaya
    Pages 227-262

  7. Numerical Approach

    • Inna Shingareva, Carlos Lizárraga-Celaya
    Pages 263-304

  8. Analytical-Numerical Approach

    • Inna Shingareva, Carlos Lizárraga-Celaya
    Pages 305-324

  9. Back Matter

    Pages 325-357
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Keywords

About this book

The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).

Reviews

From the reviews:

“The authors consider the problem of constructing closed-form and approximate solutions to nonlinear partial differential equations with the help of computer algebra systems. … The book will be useful for readers who want to try modern methods for solving nonlinear partial differential equations on concrete examples without bothering too much about the mathematics behind the methods. Thus it is mainly of interest for applied scientists. Mathematicians may use it in connection with more theoretical works; some references are given throughout the book.” (Werner M. Seiler, Zentralblatt MATH, Vol. 1233, 2012)

Authors and Affiliations

  • , Dept. of Mathematics, University of Sonora, Sonora, Mexico

    Inna Shingareva

  • , Departamento de Física, Universidad de Sonora, Sonora, Mexico

    Carlos Lizárraga-Celaya

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