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若干偏微分方程与代数偏微分方程的保结构算法

Abstract (in Chinese)第8-10页
Abstract (in English)第10-11页
Introduction第12-19页
Chapter 1 Preliminaries第19-27页
    1.1 Hamiltonian ODEs and symplectic integrator第19-21页
    1.2 Multi-symplectic Hamiltonian system and local structure-preserving algorithms第21-23页
    1.3 Differential algebraic equations第23-24页
    1.4 Partial differential algebraic equations第24-27页
Chapter 2 Explicit symplectic Fourier pseudospectral method for the KGSequation第27-47页
    2.1 New explicit scheme of KGS equation第30-35页
        2.1.1 Semi-discretization in space第30-32页
        2.1.2 Full discretization in time第32-33页
        2.1.3 Composition method第33-35页
    2.2 Numerical analysis of the scheme第35-38页
        2.2.1 Structure-Preserving properties第35-36页
        2.2.2 Linear stability analysis第36-38页
    2.3 Numerical experiments第38-44页
    2.4 Conclusions第44-47页
Chapter 3 Local energy-preserving algorithm for the BBM equation第47-64页
    3.1 Local energy-preserving algorithm第49-55页
        3.1.1 Operator definitions and properties第49-50页
        3.1.2 Multisymplectic structure of the BBM equation第50-51页
        3.1.3 Local energy-preserving algorithm第51-55页
    3.2 Numerical experiments第55-61页
    3.3 Conclusions第61-64页
Chapter 4 Local structure-preserving algorithms for the RLW equation第64-81页
    4.1 Multisymplectic structure of the RLW equation第66-69页
    4.2 Local structure-preserving schemes第69-75页
        4.2.1 Local momentum-preserving scheme第69-72页
        4.2.2 Local energy-preserving scheme第72-75页
    4.3 Numerical experiments第75-80页
    4.4 Conclusions第80-81页
Chapter 5 Fourier pseudospectral method for PDAEs第81-101页
    5.1 Fourier-pseudospectral-Crank-Nicolson scheme第82-88页
        5.1.1 Space discretization第82-85页
        5.1.2 Time discretization第85-88页
    5.2 Convergence analysis of the full discrete scheme第88-92页
    5.3 Numerical experiments第92-99页
    5.4 Conclusions第99-101页
Chapter 6 Crank-Nicolson Galerkin method for PDAEs第101-120页
    6.1 Crank-Nicolson Galerkin scheme第101-107页
        6.1.1 Space discretization第101-105页
        6.1.2 Time discretization第105-107页
    6.2 Convergence analysis of the full discrete scheme第107-111页
    6.3 Numerical experiments第111-119页
    6.4 Conclusions第119-120页
Bibliography第120-130页
Publications and Finished Papers第130-131页
Acknowledgements第131页

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