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Mathematics - Dynamical Systems & Differential Equations | Solving Nonlinear Partial Differential Equations with Maple and Mathematica

Solving Nonlinear Partial Differential Equations with Maple and Mathematica

Shingareva, Inna, Lizárraga-Celaya, Carlos

2011, XIII, 357 p.

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  • Presents different approaches for solving nonlinear PDEs and systems
  • Contains numerous examples and comparisons
  • Explores the use of two computer algebra systems, Maple and Mathematica, enables comparisons between various types of solutions and approaches
  • Presented in a concise and tutorial programming style of Maple and Mathematica that helps readers understand and solve nonlinear PDEs and many other differential equations
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

Content Level » Research

Keywords » CAS - Computer Algebra System - Maple and Mathematica - Nonlinear Partial Differential Equations - PDE

Related subjects » Computational Intelligence and Complexity - Dynamical Systems & Differential Equations - Statistical Physics & Dynamical Systems

Table of contents 

1 Introduction 1.1 Basic Concepts 2 Algebraic Approach 2.1 Point Transformations 2.2 Contact Transformations 2.3 Transformations Relating Differential Equations 2.4 Linearizing and Bilinearizing Transformations 2.5 Reductions of Nonlinear PDEs 2.6 Separation of Variables 2.7 Transformation Groups 2.8 Nonlinear Systems 3 Geometric-Qualitative Approach 3.1 Method of Characteristics 3.2 Generalized Method of Characteristics 3.3 Qualitative Analysis 4 General Analytical Approach. Integrability 4.1 Painlevé Test and Integrability 4.2 Complete Integrability. Evolution Equations 4.3 Nonlinear Systems. Integrability Conditions 5 Approximate Analytical Approach 5.1 Adomian Decomposition Method 5.2 Asymptotic Expansions. Perturbation Methods 6 Numerical Approach 6.1 Embedded Numerical Methods 6.2 Finite DifferenceMethods 7 Analytical-Numerical Approach 7.1 Method of Lines 7.2 Spectral Collocation Method;  A Brief Description of Maple A.1 Introduction A.2 Basic Concepts A.3 Maple Language B Brief Description of Mathematica B.1 Introduction B.2 Basic Concepts B.3 Mathematica Language; References, Index

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