Synopses & Reviews
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
Review
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)
Synopsis
The emphasis of the book is given
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
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
Synopsis
The emphasis of the book is given
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