This paper concentrates on the differential transform method (DTM) to solve some delay differential equations (DDEs). Based on the method of steps for DDEs and using the computer algebra system Mathematica, we success...This paper concentrates on the differential transform method (DTM) to solve some delay differential equations (DDEs). Based on the method of steps for DDEs and using the computer algebra system Mathematica, we successfully apply DTM to find the analytic solution to some DDEs, including a neural delay differential equation. The results confirm the feasibility and efficiency of DTM.展开更多
We study rogue waves described by nonlinear Schr6dinger equations. Such wave solutions are so different from conventional soliton solutions that classic methods such as the Crank-Nicolson scheme cannot work for these ...We study rogue waves described by nonlinear Schr6dinger equations. Such wave solutions are so different from conventional soliton solutions that classic methods such as the Crank-Nicolson scheme cannot work for these cases. Fortunately, we find that the local discontinuous Galerkin method equipped with Dirichlet boundary conditions can simulate rogue waves very well. Several numerical examples are presented to show such interesting wave solutions.展开更多
The two-dimensional primitive equations with Lévy noise are studied in this paper.We prove the existence and uniqueness of the solutions in a fixed probability space which based on a priori estimates,weak converg...The two-dimensional primitive equations with Lévy noise are studied in this paper.We prove the existence and uniqueness of the solutions in a fixed probability space which based on a priori estimates,weak convergence method and monotonicity arguments.展开更多
In this paper,we study the Camassa-Holm equation and the Degasperis-Procesi equation.The two equations are in the family of integrable peakon equations,and both have very rich geometric properties.Based on these geome...In this paper,we study the Camassa-Holm equation and the Degasperis-Procesi equation.The two equations are in the family of integrable peakon equations,and both have very rich geometric properties.Based on these geometric structures,we construct the geometric numerical integrators for simulating their soliton solutions.The Camassa-Holm equation and the Degasperis-Procesi equation have many common properties,however they also have the significant difference,for example there exist the shock wave solutions for the Degasperis-Procesi equation.By using the symplectic Fourier pseudo-spectral integrator,we simulate the peakon solutions of the two equations.To illustrate the smooth solitons and shock wave solutions of the DP equation,we use the splitting technique and combine the composition methods.In the numerical experiments,comparisons of these two kinds of methods are presented in terms of accuracy,computational cost and invariants preservation.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
文摘This paper concentrates on the differential transform method (DTM) to solve some delay differential equations (DDEs). Based on the method of steps for DDEs and using the computer algebra system Mathematica, we successfully apply DTM to find the analytic solution to some DDEs, including a neural delay differential equation. The results confirm the feasibility and efficiency of DTM.
基金＊Supported by the National Natural Science Foundation of China under Grant Nos 11271195, 11271196 and 41231173, the Jiangsu Collaborative Innovation Center for Climate Change, and the Project of Graduate Education Innovation of Jiangsu Province under Grant No CXZZ12-0385.
文摘We study rogue waves described by nonlinear Schr6dinger equations. Such wave solutions are so different from conventional soliton solutions that classic methods such as the Crank-Nicolson scheme cannot work for these cases. Fortunately, we find that the local discontinuous Galerkin method equipped with Dirichlet boundary conditions can simulate rogue waves very well. Several numerical examples are presented to show such interesting wave solutions.
基金supported in part by National Natural Science Foundation of China(Grant Nos. 11028102,11126303 and 11171158)Major Program of National Natural Science Foundation of China(Grant No. 91130005)+3 种基金National Basic Research Program of China (973 Program) (Grant No. 2013CB834100)Natural Science Foundation of Jiangsu Province (Grant No. BK2011777)Natural Science Foundation of Jiangsu Education Committee (Grant No. 11KJA110001)Qing Lan and "333" Project of Jiangsu Province
文摘The two-dimensional primitive equations with Lévy noise are studied in this paper.We prove the existence and uniqueness of the solutions in a fixed probability space which based on a priori estimates,weak convergence method and monotonicity arguments.
基金This research was supported by the National Natural Science Foundation of China 11271357,11271195 and 41504078by the CSC,the Foundation for Innovative Research Groups of the NNSFC 11321061 and the ITER-China Program 2014GB124005。
文摘In this paper,we study the Camassa-Holm equation and the Degasperis-Procesi equation.The two equations are in the family of integrable peakon equations,and both have very rich geometric properties.Based on these geometric structures,we construct the geometric numerical integrators for simulating their soliton solutions.The Camassa-Holm equation and the Degasperis-Procesi equation have many common properties,however they also have the significant difference,for example there exist the shock wave solutions for the Degasperis-Procesi equation.By using the symplectic Fourier pseudo-spectral integrator,we simulate the peakon solutions of the two equations.To illustrate the smooth solitons and shock wave solutions of the DP equation,we use the splitting technique and combine the composition methods.In the numerical experiments,comparisons of these two kinds of methods are presented in terms of accuracy,computational cost and invariants preservation.
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.
