Recent advances in applied nonlinear dynamics with numerical analysis [[electronic resource] ] : fractional dynamics, network dynamics, classical dynamics and fractal dynamics with their numerical simulations / / editors, Changpin Li, Yujiang Wu, Ruisong Ye

• Pubblicazione: Singapore, : World Scientific Pub. Co., 2013
• Descrizione fisica: 1 online resource (414 p.)
• Disciplina: 515.355
• Soggetto topico: Dynamics - Mathematics; Nonlinear theories - Mathematics
• Soggetto genere / forma: Electronic books.
• Altri autori: LiChangpin WuYujiang YeRuisong
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Preface; Foreword; Contents; 1. Gronwall inequalities Fanhai Zeng, Jianxiong Cao and Changpin Li; 1.1 Introduction; 1.2 The continuous Gronwall inequalities; 1.3 The discrete Gronwall inequalities; 1.4 The weakly singular Gronwall inequalities; 1.5 Conclusion; Bibliography; 2. Existence and uniqueness of the solutions to the fractional differential equations Yutian Ma, Fengrong Zhang and Changpin Li; 2.1 Introduction; 2.2 Preliminaries and notations; 2.3 Existence and uniqueness of initial value problems for fractional differential equations ; 2.3.1 Initial value problems with Riemann-Liouville derivative2.3.2 Initial value problems with Caputo derivative; 2.3.3 The positive solution to fractional differential equation; 2.4 Existence and uniqueness of the boundary value problems; 2.4.1 Boundary value problems with Riemann-Liouville derivative; 2.4.2 Boundary value problems with Caputo derivative; 2.4.3 Fractional differential equations with impulsive boundary conditions; 2.5 Existence and uniqueness of the fractional differential equations with time-delay; 2.6 Conclusions; Bibliography ; 3. Finite element methods for fractional differential equations Changpin Li and Fanhai Zeng3.1 Introduction; 3.2 Preliminaries and notations; 3.3 Finite element methods for fractional differential equations; 3.4 Conclusion; Bibliography; 4. Fractional step method for the nonlinear conservation laws with fractional dissipation Can Li and Weihua Deng; 4.1 Introduction; 4.2 Fractional step algorithm; 4.2.1 Discretization of the fractional calculus; 4.2.2 Discretization of the conservation law; 4.3 Numerical results; 4.4 Concluding remarks; Bibliography ; 5. Error analysis of spectral method for the space and time fractional Fokker-Planck equation Tinggang Zhao and Haiyan Xuan5.1 Introduction; 5.2 Preliminaries; 5.3 Spectral method; 5.4 Stability and convergence; 5.4.1 Semi-discrete of space spectral method; 5.4.2 The time discretization of Caputo derivative; 5.5 Fully discretization and its error analysis; 5.6 Conclusion remarks; Bibliography; 6. A discontinuous finite element method for a type of fractional Cauchy problem Yunying Zheng; 6.1 Introduction; 6.2 Fractional derivative space ; 6.3 The discontinuous Galerkin finite element approximation6.4 Error estimation; 6.5 Numerical examples; 6.6 Conclusion; Bibliography; 7. Asymptotic analysis of a singularly perturbed parabolic problem in a general smooth domain Yu-Jiang Wu, Na Zhang and Lun-Ji Song; 7.1 Introduction; 7.2 The curvilinear coordinates; 7.3 Asymptotic expansion; 7.3.1 Global expansion; 7.3.2 Boundary corrector; 7.3.3 Estimates of the solutions of boundary layer equations; 7.4 Error estimate; 7.5 An example; Bibliography ; 8. Incremental unknowns methods for the ADI and ADSI schemes Ai-Li Yang, Yu-Jiang Wu and Zhong-Hua Yang
• Sommario/riassunto: 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 w
• Titolo autorizzato: Recent advances in applied nonlinear dynamics with numerical analysis
• ISBN: 1-299-46265-0; 981-4436-46-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910452341903321
• Lo trovi qui: Univ. Federico II
• Serie: Interdisciplinary mathematical sciences ; ; v. 15.