In the paper,we propose a novel linearly implicit structure-preserving algorithm,which is derived by combing the invariant energy quadratization approach with the exponential time differencing method,to construct effi...In the paper,we propose a novel linearly implicit structure-preserving algorithm,which is derived by combing the invariant energy quadratization approach with the exponential time differencing method,to construct efficient and accurate time discretization scheme for a large class of Hamiltonian partial differential equations(PDEs).The proposed scheme is a linear system,and can be solved more efficient than the original energy-preserving ex-ponential integrator scheme which usually needs nonlinear iterations.Various experiments are performed to verify the conservation,efficiency and good performance at relatively large time step in long time computations.展开更多
Discusses the symplectic integration of separable Hamiltonian ordinary and partial differential equations (PDE). Results of a von Neumann analysis; Spectra of linearized Hamiltonian PDEs.
基金supported by the National Natural Science Foundation of China(Grant Nos.12171245,11971416,11971242,12301508)by the Natural Science Foundation of Henan Province(Grant No.222300420280)+1 种基金by the Natural Science Foundation of Hunan Province(Grant No.2023JJ40656)by the Scientific Research Fund of Xuchang University(Grant No.2024ZD010).
文摘In the paper,we propose a novel linearly implicit structure-preserving algorithm,which is derived by combing the invariant energy quadratization approach with the exponential time differencing method,to construct efficient and accurate time discretization scheme for a large class of Hamiltonian partial differential equations(PDEs).The proposed scheme is a linear system,and can be solved more efficient than the original energy-preserving ex-ponential integrator scheme which usually needs nonlinear iterations.Various experiments are performed to verify the conservation,efficiency and good performance at relatively large time step in long time computations.
文摘Discusses the symplectic integration of separable Hamiltonian ordinary and partial differential equations (PDE). Results of a von Neumann analysis; Spectra of linearized Hamiltonian PDEs.
