The fourth order average vector field(AVF)method is applied to solve the“Good”Boussinesq equation.The semi-discrete system of the“good”Boussi-nesq equation obtained by the pseudo-spectral method in spatial variabl...The fourth order average vector field(AVF)method is applied to solve the“Good”Boussinesq equation.The semi-discrete system of the“good”Boussi-nesq equation obtained by the pseudo-spectral method in spatial variable,which is a classical finite dimensional Hamiltonian system,is discretizated by the fourth order average vector field method.Thus,a new high order energy conservation scheme of the“good”Boussinesq equation is obtained.Numerical experiments confirm that the new high order scheme can preserve the discrete energy of the“good”Boussinesq equation exactly and simulate evolution of different solitary waves well.展开更多
In this paper,a conformal energy-conserved scheme is proposed for solving the Maxwell’s equations with the perfectly matched layer.The equations are split as a Hamiltonian system and a dissipative system,respectively...In this paper,a conformal energy-conserved scheme is proposed for solving the Maxwell’s equations with the perfectly matched layer.The equations are split as a Hamiltonian system and a dissipative system,respectively.The Hamiltonian system is solved by an energy-conserved method and the dissipative system is integrated exactly.With the aid of the Strang splitting,a fully-discretized scheme is obtained.The resulting scheme can preserve the five discrete conformal energy conservation laws and the discrete conformal symplectic conservation law.Based on the energy method,an optimal error estimate of the scheme is established in discrete L2-norm.Some numerical experiments are addressed to verify our theoretical analysis.展开更多
基金supported by the Innovative Science Research Project for Grad-uate Students of Hainan Province(Grant Nos.Hys2014-17)the Visiting Project of Hainan University and the Fostering Program of Excellent Dissertation for the Gradu-ate Students of Hainan University,the Natural Science Foundation of China(Grant Nos.11161017,11561018)+1 种基金the National Science Foundation of Hainan Province(Grant Nos.114003)the Training Programs of Innovation and Entrepreneurship for Under-graduates of Hainan University.
文摘The fourth order average vector field(AVF)method is applied to solve the“Good”Boussinesq equation.The semi-discrete system of the“good”Boussi-nesq equation obtained by the pseudo-spectral method in spatial variable,which is a classical finite dimensional Hamiltonian system,is discretizated by the fourth order average vector field method.Thus,a new high order energy conservation scheme of the“good”Boussinesq equation is obtained.Numerical experiments confirm that the new high order scheme can preserve the discrete energy of the“good”Boussinesq equation exactly and simulate evolution of different solitary waves well.
基金supported by the National Natural Science Foundation of China(Grant Nos.11771213,41504078)the National Key Research and Development Project of China(Grant No.2016YFC0600310)+2 种基金supported by National Key R&D Program of the Ministry of Science and Technology of China with the Project"Integration Platform Construction for Joint Inversion and Interpretation of Integrated Geophysics"(Grant No.2018YFC0603500)the Major Projects of Natural Sciences of University in Jiangsu Province of China(Grant No.15KJA110002)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘In this paper,a conformal energy-conserved scheme is proposed for solving the Maxwell’s equations with the perfectly matched layer.The equations are split as a Hamiltonian system and a dissipative system,respectively.The Hamiltonian system is solved by an energy-conserved method and the dissipative system is integrated exactly.With the aid of the Strang splitting,a fully-discretized scheme is obtained.The resulting scheme can preserve the five discrete conformal energy conservation laws and the discrete conformal symplectic conservation law.Based on the energy method,an optimal error estimate of the scheme is established in discrete L2-norm.Some numerical experiments are addressed to verify our theoretical analysis.
