Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically...

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Hlavný autor: Wu, Xinyuan (Autor)
Médium: Elektronický zdroj E-kniha
Jazyk:English
Vydavateľské údaje: Singapore : Springer Singapore , 2018.
Vydanie:1st ed. 2018.
Predmet:
Algorithms.
Computational complexity.
ISBN:9789811090042
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Obsah:
  • Functionally fitted continuous finite element methods for oscillatory Hamiltonian system
  • Exponential average-vector-field integrator for conservative or dissipative systems
  • Exponential Fourier collocation methods for first-order differential Equations
  • Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems
  • High-order symplectic and symmetric composition integrators for multi-frequency oscillatory Hamiltonian systems
  • The construction of arbitrary order ERKN integrators via group theory
  • Trigonometric collocation methods for multi-frequency and multidimensional oscillatory systems
  • A compact tri-colored tree theory for general ERKN methods
  • An integral formula adapted to different boundary conditions for arbitrarily high-dimensional nonlinear Klein-Gordon equations
  • An energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations
  • Arbitrarily high-order time-stepping schemes for nonlinear Klein-Gordon equations
  • An essential extension of the finite-energy condition for ERKN integrators solving nonlinear wave equations
  • Index.

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