TY - JOUR
T1 - The Time High-Order Energy-Preserving Schemes for the Nonlocal Benjamin-Ono Equation
AU - Chen , Chunguang
AU - Liang , Dong
AU - Xie , Shusen
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 543
EP - 556
PY - 2020
DA - 2020/08
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/17869.html
KW - Nonlocal Benjamin-Ono equation, Hamiltonian boundary value method (HBVM),
time high-order, energy preserving, Fourier pseudospectral method.
AB - <p style="text-align: justify;">The new time high-order energy-preserving schemes are proposed for the nonlocal
Benjamin-Ono equation. We get the Hamiltonian system to the nonlocal model, and it is then
discretized by a Fourier pseudospectral method in space and the Hamiltonian boundary value
method (HBVM) in time. This approach has high order of convergence in time and conserves the
total mass and energy in discrete forms. We further develop a time second-order energy-preserving
scheme and a time fourth-order energy-preserving scheme for the nonlocal Benjamin-Ono equation.
Numerical experiments test the proposed schemes with a single solitary wave and the interaction
of two solitary waves. Results confirm the accuracy and conservation properties of the schemes.</p>