Multi-symplectic Runge–Kutta-type methods for Hamiltonian wave equations
暂无分享,去创建一个
[1] Theodor Meis,et al. Numerical solution of partial differential equations , 1981 .
[2] Ernst Hairer,et al. The numerical solution of differential-algebraic systems by Runge-Kutta methods , 1989 .
[3] David R. Basco,et al. Computational fluid dynamics - an introduction for engineers , 1989 .
[4] R. Ruth,et al. Fourth-order symplectic integration , 1990 .
[5] Wojciech Rozmus,et al. A symplectic integration algorithm for separable Hamiltonian functions , 1990 .
[6] J. M. Sanz-Serna,et al. Numerical Hamiltonian Problems , 1994 .
[7] T. Bridges. A geometric formulation of the conservation of wave action and its implications for signature and the classification of instabilities , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[8] T. Bridges. Multi-symplectic structures and wave propagation , 1997, Mathematical Proceedings of the Cambridge Philosophical Society.
[9] J. Marsden,et al. Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs , 1998, math/9807080.
[10] Jerrold E. Marsden,et al. Multisymplectic geometry, covariant Hamiltonians, and water waves , 1998, Mathematical Proceedings of the Cambridge Philosophical Society.
[11] Thomas J. Bridges,et al. Unstable eigenvalues and the linearization about solitary waves and fronts with symmetry , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[12] Sebastian Reich,et al. Finite Volume Methods for Multi-Symplectic PDES , 2000 .
[13] S. Reich. Multi-Symplectic Runge—Kutta Collocation Methods for Hamiltonian Wave Equations , 2000 .
[14] M. Qin,et al. Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation , 2000 .
[15] S. Reich,et al. Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity , 2001 .
[16] S. Reich,et al. Multi-symplectic spectral discretizations for the Zakharov–Kuznetsov and shallow water equations , 2001 .
[17] Thomas J. Bridges,et al. Linear Instability of Solitary Wave Solutions of the Kawahara Equation and Its Generalizations , 2002, SIAM J. Math. Anal..
[18] Thomas J. Bridges,et al. Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework , 2002 .
[19] Ying Liu,et al. A novel numerical approach to simulating nonlinear Schro"dinger equations with varying coefficients , 2003, Appl. Math. Lett..
[20] U. Ascher,et al. Multisymplectic box schemes and the Korteweg{de Vries equation , 2004 .
[21] Brian E. Moore. A modified equations approach for multi-symplectic integration methods. , 2003 .
[22] Brian E. Moore,et al. Backward error analysis for multi-symplectic integration methods , 2003, Numerische Mathematik.
[23] GengSun,et al. SYMPLECTIC RK METHODS AND SYMPLECTIC PRK METHODS WITH REAL EIGENVALUES , 2004 .
[24] Jialin Hong,et al. Spurious behavior of a symplectic integrator , 2005 .
[25] Geng Sun,et al. The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs , 2005, Math. Comput..
[26] E. Hairer,et al. Geometric Numerical Integration , 2022, Oberwolfach Reports.