TY - JOUR
T1 - An Energy-Preserving Wavelet Collocation Method for General Multi-Symplectic Formulations of Hamiltonian PDEs
JO - Communications in Computational Physics
VL - 5
SP - 1313
EP - 1339
PY - 2018
DA - 2018/04
SN - 20
DO - http://doi.org/10.4208/cicp.231014.110416a
UR - https://global-sci.org/intro/article_detail/cicp/11191.html
KW - 
AB - <p style="text-align: justify;">In this paper, we develop a novel energy-preserving wavelet collocation
method for solving general multi-symplectic formulations of Hamiltonian PDEs. Based
on the autocorrelation functions of Daubechies compactly supported scaling functions,
the wavelet collocation method is conducted for spatial discretization. The obtained
semi-discrete system is shown to be a finite-dimensional Hamiltonian system, which
has an energy conservation law. Then, the average vector field method is used for
time integration, which leads to an energy-preserving method for multi-symplectic
Hamiltonian PDEs. The proposed method is illustrated by the nonlinear Schrödinger
equation and the Camassa-Holm equation. Since differentiation matrix obtained by
the wavelet collocation method is a cyclic matrix, we can apply Fast Fourier transform
to solve equations in numerical calculation. Numerical experiments show the high
accuracy, effectiveness and conservation properties of the proposed method.</p>