eBook Recent Advances In Applied Nonlinear Dynamics With Numerical Analysis: Fractional Dynamics, Network Dynamics, Classical Dynamics And Fractal Dynamics With Their Numerical Simulations, 1st Edition

  • Published By: World Scientific Publishing Company
  • ISBN-10: 9814436461
  • ISBN-13: 9789814436465
  • DDC: 515.355
  • Grade Level Range: College Freshman - College Senior
  • 416 Pages | eBook
  • Original Copyright 2013 | Published/Released January 2015
  • This publication's content originally published in print form: 2013
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About

Overview

Nonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation.Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations will be introduced and discussed.In the infinite dimensional dynamics part, we emphasize on numerical calculation and theoretical analysis, including constructing various numerical methods and computing the corresponding limit sets, etc.In the last part, we show interest in network dynamics and fractal dynamics together with numerical simulations as well as their applications.

Table of Contents

Front Cover.
Half Title Page.
Other Frontmatter.
Title Page.
Copyright Page.
Frontispiece.
Foreword.
Preface.
Contents.
1: Gronwall Inequalities.
Bibliography.
2: Existence and Uniqueness of the Solutions to the Fractional Differential Equations.
Bibliography.
3: Finite Element Methods for Fractional Differential Equations.
Bibliography.
4: Fractional Step Method for the Nonlinear Conservation Laws with Fractional Dissipation.
Bibliography.
5: Error Analysis of Spectral Method for the Space and Time Fractional Fokker–Planck Equation.
Bibliography.
6: A Discontinuous Finite Element Method for a Type of Fractional Cauchy Problem.
Bibliography.
7: Asymptotic Analysis of a Singularly Perturbed Parabolic Problem in a General Smooth Domain.
Bibliography.
8: Incremental Unknowns Methods for the Alternating Directional Implicit and Semi-implicit Schemes.
Bibliography.
9: Stability of A Colocated Finite Volume Scheme for the 3D Incompressible Navier-Stokes Equations.
Bibliography.
10: Computing the Multiple Positive Solutions to P-Henon Equation on the Unit Square.
Bibliography.
11: Multilevel Wavelet-like Block Incremental Unknowns Methods for a Class of Reaction-Diffusion Equations.
Bibliography.
12: Models and Dynamics of Deterministically Growing Networks.
Bibliography.
13: On Different Approaches to Synchronization of Spatiotemporal Chaos in Complex Networks: a Case Study.
Bibliography.
14: Chaotic Dynamical Systems on Fractals and Their Applications to Image Encryption.
Bibliography.
15: Planar Crystallographic Symmetric Tiling Patterns Generated From Invariant Maps.
Bibliography.
16: Complex Dynamics in a Simple Two-Dimensional Discrete System.
Bibliography.
17: Approximate Periodic Solutions of Damped Harmonic Oscillators With Delayed Feedback.
Bibliography.
18: The Numerical Methods in Option Pricing Problem.
Bibliography.
19: Synchronization and Its Control Between Two Coupled Networks.
Bibliography.
Index.