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Solving Nonlinear Partial Differential Equations with Maple and Mathematica

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Solving Nonlinear Partial Differential Equations with Maple and Mathematica Cover

 

Synopses & Reviews

Publisher Comments:

The emphasis of this work is on constructing 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

Synopsis:

This volume shows how to construct solutions of numerous nonlinear PDEs quickly and easily. The text discusses comparisons and relationships between the varying solutions, methods and approaches.

Synopsis:

The emphasis of the book is given

Table of Contents

1 General Analytical Approach 1.1 Classification of PDEs 1.2 Analytical Solutions 1.3 Transformations of Nonlinear PDEs 1.4 Traveling-Wave Solutions 1.5 Self-Similar Solutions 1.6 Separable Solutions 1.7 Differential constraints 1.8 Applications of the Painlev Test 2 Geometric Approach 2.1 Method of Characteristics 2.2 Generalized Method of Characteristics 2.3 Method of Characteristics and Conservation Laws 2.4 Direction Fields 2.5 Integral Surfaces 2.6 Poincar Sections 3 Algebraic Approach 3.1 One-Parameter Group of Transformations 3.2 Group Analysis for Nonlinear PDEs 3.3 Invariant Solutions 4 Transform Approach 4.1 Inverse Scattering Transform Approach 5 Systems of nonlinear PDEs. Analytical approach 5.1 Overdetermined systems 5.2 Pfaffian equations and overdetermined systems 5.3 Transformations of nonlinear systems 5.4 Traveling wave solutions 5.5 Generalized separation of variables 6 Approximate Analytical Approach 6.1 Asymptotic traveling wave solution 6.2 Asymptotic solution of Cauchy problem 6.3 Asymptotic solution of systems of nonlinear PDEs 7 Qualitative Approach 7.1 Traveling wave solutions 7.2 Asymptotic solutions 8 Numerical Approach 8.1 Numerical and Graphical Solutions 8.2 Finite Difference Methods 9 Analytical-Numerical Approach 9.1 Spectral Collocation Methods 9.2 Finite Element Methods 9.3 Boundary Element Methods Supplement A. Foundations of Maple Basic Concepts Maple Language Supplement B. Foundations of Mathematica Basic Concepts Mathematica Language References General Index Maple Index Mathematica Index

Product Details

ISBN:
9783709105160
Author:
Shingareva, Inna
Publisher:
Springer
Author:
Shingareva, Inna K.
Author:
Lizrraga-Celaya, Carlos
Author:
Lizarraga-Celaya, Carlos
Subject:
Differential Equations
Subject:
écas
Subject:
computer algebra system
Subject:
Maple and Mathematica
Subject:
nonlinear partial differential equations
Subject:
PDE
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
Nonlinear Dynamics.
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
Mathematics-Applied
Copyright:
Edition Description:
2011
Publication Date:
20110829
Binding:
HARDCOVER
Language:
English
Pages:
370
Dimensions:
235 x 155 mm

Related Subjects


Reference » Science Reference » Technology
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Computer
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Popular Chaos and Fractals

Solving Nonlinear Partial Differential Equations with Maple and Mathematica New Hardcover
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$124.00 In Stock
Product details 370 pages Springer - English 9783709105160 Reviews:
"Synopsis" by , This volume shows how to construct solutions of numerous nonlinear PDEs quickly and easily. The text discusses comparisons and relationships between the varying solutions, methods and approaches.
"Synopsis" by , The emphasis of the book is given
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