LEADER 05613nam 2200697 a 450 001 9910452341903321 005 20200520144314.0 010 $a1-299-46265-0 010 $a981-4436-46-1 035 $a(CKB)2550000001019250 035 $a(EBL)1168134 035 $a(OCoLC)839388507 035 $a(SSID)ssj0000908535 035 $a(PQKBManifestationID)11525378 035 $a(PQKBTitleCode)TC0000908535 035 $a(PQKBWorkID)10901539 035 $a(PQKB)10739419 035 $a(MiAaPQ)EBC1168134 035 $a(WSP)00002940 035 $a(PPN)189428341 035 $a(Au-PeEL)EBL1168134 035 $a(CaPaEBR)ebr10691978 035 $a(CaONFJC)MIL477515 035 $a(EXLCZ)992550000001019250 100 $a20130507d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aRecent advances in applied nonlinear dynamics with numerical analysis$b[electronic resource] $efractional dynamics, network dynamics, classical dynamics and fractal dynamics with their numerical simulations /$feditors, Changpin Li, Yujiang Wu, Ruisong Ye 210 $aSingapore $cWorld Scientific Pub. Co.$d2013 215 $a1 online resource (414 p.) 225 1 $aInterdisciplinary mathematical sciences ;$vv. 15 300 $aDescription based upon print version of record. 311 $a981-4436-45-3 320 $aIncludes bibliographical references and index. 327 $aPreface; 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 327 $a2.3.1 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 327 $a3. 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 327 $a5. 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 327 $a6.3 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 327 $a8. Incremental unknowns methods for the ADI and ADSI schemes Ai-Li Yang, Yu-Jiang Wu and Zhong-Hua Yang 330 $aNonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation.Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations w 410 0$aInterdisciplinary mathematical sciences ;$vv. 15. 606 $aDynamics$xMathematics 606 $aNonlinear theories$xMathematics 608 $aElectronic books. 615 0$aDynamics$xMathematics. 615 0$aNonlinear theories$xMathematics. 676 $a515.355 701 $aLi$b Changpin$0928623 701 $aWu$b Yujiang$0928624 701 $aYe$b Ruisong$0928625 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910452341903321 996 $aRecent advances in applied nonlinear dynamics with numerical analysis$92087026 997 $aUNINA