Nonlinear Physics with Maple for Scientists and Engineers [E-Book] / by Richard H. Enns, George McGuire.
Philosophy of the Text This text has been designed to be an introductory survey of the basic concepts and applied mathematical methods of nonlinear science. Students in engineer ing, physics, chemistry, mathematics, computing science, and biology should be able to successfully use this text. In an...
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Full text |
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Personal Name(s): | Enns, Richard H., author |
McGuire, George, author | |
Imprint: |
Boston, MA :
Birkhäuser,
1997
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Physical Description: |
online resource. |
Note: |
englisch |
ISBN: |
9781468400328 |
DOI: |
10.1007/978-1-4684-0032-8 |
Subject (LOC): |
- 1 Introduction
- 1.1 It’s a Nonlinear World
- 1.2 Symbolic Computation
- 1.3 Nonlinear Activities
- 1.4 Structure of the Text
- 2 Some Nonlinear Systems
- 2.1 Nonlinear Mechanics
- 2.2 Competition Phenomena
- 2.3 Nonlinear Electrical Phenomena
- 2.4 Chemical and Other Oscillators
- 2.5 Pattern Formation
- 2.6 Solitons
- 2.7 Chaos and Maps
- 3 Topological Analysis
- 3.1 Introductory Remarks
- 3.2 Types of Simple Singular Points
- 3.3 Classifying Simple Singular Points
- 3.4 Examples of Phase Plane Analysis
- 3.5 Isoclines
- 4 Analytic Methods
- 4.1 Introductory Remarks
- 4.2 Some Exact Methods
- 4.3 Some Approximate Methods
- 4.4 The Krylov-Bogoliubov (KB) Method
- 4.5 Ritz and Galerkin Methods
- 5 The Numerical Approach
- 5.1 Finite-Difference Approximations
- 5.2 Euler and Modified Euler Methods
- 5.3 Rungé-Kutta (RK) Methods
- 5.4 Adaptive Step Size
- 5.5 Stiff Equations
- 5.6 Implicit and Semi-Implicit Schemes
- 6 Limit Cycles
- 6.1 Stability Aspects
- 6.2 Relaxation Oscillations
- 6.3 Bendixson’s First Theorem: The Negative Criterion
- 6.4 The Poincaré-Bendixson Theorem
- 6.5 The Brusselator Model
- 7 Forced Oscillators
- 7.1 Duffing’s Equation
- 7.2 The Jump Phenomenon and Hysteresis
- 7.3 Subharmonic and Other Periodic Oscillations
- 7.4 Power Spectrum
- 7.5 Chaotic Oscillations
- 7.6 Entrainment and Quasiperiodicity
- 7.7 The Rössler and Lorenz Systems
- 8 Nonlinear Maps
- 8.1 Introductory Remarks
- 8.2 The Logistic Map
- 8.3 Fixed Points and Stability
- 8.4 The Period-Doubling Cascade to Chaos
- 8.5 Period Doubling in the Real World
- 8.6 The Lyapunov Exponent
- 8.7 Stretching and Folding
- 8.8 The Circle Map
- 8.9 Chaos versus Noise
- 8.10 2-Dimensional Maps
- 9 Nonlinear PDE Phenomena
- 9.1 Introductory Remarks
- 9.2 Burger’s Equation
- 9.3 Bäcklund Transformations
- 9.4 Solitary Waves
- 10 Numerical Simulation
- 10.1 Finite Difference Approximations
- 10.2 Explicit Methods
- 10.3 Von Neumann Stability Analysis
- 10.4 Implicit Methods
- 10.5 Method of Characteristics
- 10.6 Higher Dimensions
- 11 Inverse Scattering Method
- 11.1 Lax’s Formulation
- 11.2 Application to KdV Equation
- 11.3 Multi-Soliton Solutions
- 11.4 General Input Shapes
- 11.5 The Zakharov-Shabat/AKNS Approach.