The multi-symplectic formulations of the 'Good' Boussinesq equation were considered. For the multi-symplectic formulation, a new fifteen-point difference scheme which is equivalent to the multi-symplectic Prei...The multi-symplectic formulations of the 'Good' Boussinesq equation were considered. For the multi-symplectic formulation, a new fifteen-point difference scheme which is equivalent to the multi-symplectic Preissman integrator was derived. The numerical experiments show that, the multi- symplectic scheme have excellent long-time numerical. behavior.展开更多
Aiming to solve the steering instability and hysteresis of agricultural robots in the process of movement,a fusion PID control method of particle swarm optimization(PSO)and genetic algorithm(GA)was proposed.The fusion...Aiming to solve the steering instability and hysteresis of agricultural robots in the process of movement,a fusion PID control method of particle swarm optimization(PSO)and genetic algorithm(GA)was proposed.The fusion algorithm took advantage of the fast optimization ability of PSO to optimize the population screening link of GA.The Simulink simulation results showed that the convergence of the fitness function of the fusion algorithm was accelerated,the system response adjustment time was reduced,and the overshoot was almost zero.Then the algorithm was applied to the steering test of agricultural robot in various scenes.After modeling the steering system of agricultural robot,the steering test results in the unloaded suspended state showed that the PID control based on fusion algorithm reduced the rise time,response adjustment time and overshoot of the system,and improved the response speed and stability of the system,compared with the artificial trial and error PID control and the PID control based on GA.The actual road steering test results showed that the PID control response rise time based on the fusion algorithm was the shortest,about 4.43 s.When the target pulse number was set to 100,the actual mean value in the steady-state regulation stage was about 102.9,which was the closest to the target value among the three control methods,and the overshoot was reduced at the same time.The steering test results under various scene states showed that the PID control based on the proposed fusion algorithm had good anti-interference ability,it can adapt to the changes of environment and load and improve the performance of the control system.It was effective in the steering control of agricultural robot.This method can provide a reference for the precise steering control of other robots.展开更多
Accurate prediction of flood events is important for flood control and risk management.Machine learning techniques contributed greatly to advances in flood predictions,and existing studies mainly focused on predicting...Accurate prediction of flood events is important for flood control and risk management.Machine learning techniques contributed greatly to advances in flood predictions,and existing studies mainly focused on predicting flood resource variables using single or hybrid machine learning techniques.However,class-based flood predictions have rarely been investigated,which can aid in quickly diagnosing comprehensive flood characteristics and proposing targeted management strategies.This study proposed a prediction approach of flood regime metrics and event classes coupling machine learning algorithms with clustering-deduced membership degrees.Five algorithms were adopted for this exploration.Results showed that the class membership degrees accurately determined event classes with class hit rates up to 100%,compared with the four classes clustered from nine regime metrics.The nonlinear algorithms(Multiple Linear Regression,Random Forest,and least squares-Support Vector Machine)outperformed the linear techniques(Multiple Linear Regression and Stepwise Regression)in predicting flood regime metrics.The proposed approach well predicted flood event classes with average class hit rates of 66.0%-85.4%and 47.2%-76.0%in calibration and validation periods,respectively,particularly for the slow and late flood events.The predictive capability of the proposed prediction approach for flood regime metrics and classes was considerably stronger than that of hydrological modeling approach.展开更多
This paper proposes an equivalent modeling method for photovoltaic(PV)power stations via a particle swarm optimization(PSO)K-means clustering(KMC)algorithm with passive filter parameter clustering to address the compl...This paper proposes an equivalent modeling method for photovoltaic(PV)power stations via a particle swarm optimization(PSO)K-means clustering(KMC)algorithm with passive filter parameter clustering to address the complexities,simulation time cost and convergence problems of detailed PV power station models.First,the amplitude–frequency curves of different filter parameters are analyzed.Based on the results,a grouping parameter set for characterizing the external filter characteristics is established.These parameters are further defined as clustering parameters.A single PV inverter model is then established as a prerequisite foundation.The proposed equivalent method combines the global search capability of PSO with the rapid convergence of KMC,effectively overcoming the tendency of KMC to become trapped in local optima.This approach enhances both clustering accuracy and numerical stability when determining equivalence for PV inverter units.Using the proposed clustering method,both a detailed PV power station model and an equivalent model are developed and compared.Simulation and hardwarein-loop(HIL)results based on the equivalent model verify that the equivalent method accurately represents the dynamic characteristics of PVpower stations and adapts well to different operating conditions.The proposed equivalent modeling method provides an effective analysis tool for future renewable energy integration research.展开更多
Existing feature selection methods for intrusion detection systems in the Industrial Internet of Things often suffer from local optimality and high computational complexity.These challenges hinder traditional IDS from...Existing feature selection methods for intrusion detection systems in the Industrial Internet of Things often suffer from local optimality and high computational complexity.These challenges hinder traditional IDS from effectively extracting features while maintaining detection accuracy.This paper proposes an industrial Internet ofThings intrusion detection feature selection algorithm based on an improved whale optimization algorithm(GSLDWOA).The aim is to address the problems that feature selection algorithms under high-dimensional data are prone to,such as local optimality,long detection time,and reduced accuracy.First,the initial population’s diversity is increased using the Gaussian Mutation mechanism.Then,Non-linear Shrinking Factor balances global exploration and local development,avoiding premature convergence.Lastly,Variable-step Levy Flight operator and Dynamic Differential Evolution strategy are introduced to improve the algorithm’s search efficiency and convergence accuracy in highdimensional feature space.Experiments on the NSL-KDD and WUSTL-IIoT-2021 datasets demonstrate that the feature subset selected by GSLDWOA significantly improves detection performance.Compared to the traditional WOA algorithm,the detection rate and F1-score increased by 3.68%and 4.12%.On the WUSTL-IIoT-2021 dataset,accuracy,recall,and F1-score all exceed 99.9%.展开更多
Impact craters are important for understanding the evolution of lunar geologic and surface erosion rates,among other functions.However,the morphological characteristics of these micro impact craters are not obvious an...Impact craters are important for understanding the evolution of lunar geologic and surface erosion rates,among other functions.However,the morphological characteristics of these micro impact craters are not obvious and they are numerous,resulting in low detection accuracy by deep learning models.Therefore,we proposed a new multi-scale fusion crater detection algorithm(MSF-CDA)based on the YOLO11 to improve the accuracy of lunar impact crater detection,especially for small craters with a diameter of<1 km.Using the images taken by the LROC(Lunar Reconnaissance Orbiter Camera)at the Chang’e-4(CE-4)landing area,we constructed three separate datasets for craters with diameters of 0-70 m,70-140 m,and>140 m.We then trained three submodels separately with these three datasets.Additionally,we designed a slicing-amplifying-slicing strategy to enhance the ability to extract features from small craters.To handle redundant predictions,we proposed a new Non-Maximum Suppression with Area Filtering method to fuse the results in overlapping targets within the multi-scale submodels.Finally,our new MSF-CDA method achieved high detection performance,with the Precision,Recall,and F1 score having values of 0.991,0.987,and 0.989,respectively,perfectly addressing the problems induced by the lesser features and sample imbalance of small craters.Our MSF-CDA can provide strong data support for more in-depth study of the geological evolution of the lunar surface and finer geological age estimations.This strategy can also be used to detect other small objects with lesser features and sample imbalance problems.We detected approximately 500,000 impact craters in an area of approximately 214 km2 around the CE-4 landing area.By statistically analyzing the new data,we updated the distribution function of the number and diameter of impact craters.Finally,we identified the most suitable lighting conditions for detecting impact crater targets by analyzing the effect of different lighting conditions on the detection accuracy.展开更多
This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space. Recurring to the midpoint rule, it presents an implicit multi-symplectic scheme with discrete mu...This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space. Recurring to the midpoint rule, it presents an implicit multi-symplectic scheme with discrete multi-symplectic conservation law to solve the partial differential equations which are derived from the generalized fifth-order KdV equation numerically. The results of the numerical experiments show that this multi-symplectic algorithm is good in accuracy and its long-time numerical behaviour is also perfect.展开更多
In this paper, the multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space are considered. The complex method is introduced and a semi-implicit twenty-...In this paper, the multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space are considered. The complex method is introduced and a semi-implicit twenty-seven-points scheme with certain discrete conservation laws-a multi-symplectic conservation law （CLS）, a local energy conservation law （ECL） as well as a local momentum conservation law （MCL） --is constructed to discrete the PDEs that are derived from the membrane free vibration equation. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior,展开更多
Based on splitting multi-symplectic structures, a new multi-symplectic scheme is proposed and applied to a nonlinear wave equation. The explicit multi-symplectic scheme of the nonlinear wave equation is obtained, and ...Based on splitting multi-symplectic structures, a new multi-symplectic scheme is proposed and applied to a nonlinear wave equation. The explicit multi-symplectic scheme of the nonlinear wave equation is obtained, and the corresponding multi-symplectic conservation property is proved. The backward error analysis shows that the explicit multi-symplectic scheme has good accuracy. The sine-Gordon equation and the Klein-Gordon equation are simulated by an explicit multi-symplectic scheme. The numerical results show that the new explicit multi-symplectic scheme can well simulate the solitary wave behaviors of the nonlinear wave equation and approximately preserve the relative energy error of the equation.展开更多
We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov-Kuznetsov equation. The method combines the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler ...We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov-Kuznetsov equation. The method combines the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler method for temporal discretization. It is verified that the proposed method has corresponding discrete multi-symplectic conservation laws. Numerical simulations indicate that the proposed scheme is characterized by excellent conservation.展开更多
Nonlinear wave equations have been extensively investigated in the last sev- eral decades. The Landau-Ginzburg-Higgs equation, a typical nonlinear wave equation, is studied in this paper based on the multi-symplectic ...Nonlinear wave equations have been extensively investigated in the last sev- eral decades. The Landau-Ginzburg-Higgs equation, a typical nonlinear wave equation, is studied in this paper based on the multi-symplectic theory in the Hamilton space. The multi-symplectic Runge-Kutta method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the first-order partial differential equations （PDEs） derived from the Landau-Ginzburg-Higgs equation. The numerical re- sults for the soliton solution of the Landau-Ginzburg-Higgs equation are reported, showing that the multi-symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors.展开更多
Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this pap...Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.展开更多
A conformal multi-symplectic method has been proposed for the damped Korteweg–de Vries(DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissma...A conformal multi-symplectic method has been proposed for the damped Korteweg–de Vries(DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissmann box scheme,we obtain a conformal multi-symplectic scheme for multi-symplectic partial differential equations(PDEs) with added dissipation. Applying it to the DKdV equation, we construct a conformal multi-symplectic algorithm for it, which is of second order accuracy in time. Numerical experiments demonstrate that the proposed method not only preserves the dissipation rate of mass exactly with periodic boundary conditions, but also has excellent long-time numerical behavior.展开更多
In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrtidinger-KdV equations （CS＇KE） with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospect...In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrtidinger-KdV equations （CS＇KE） with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral （MSFP） scheme for the CSKE. In numerical experiments, we compare the MSFP method with the Crank-Nicholson （CN） method. Our results show high accuracy, effectiveness, and good ability of conserving the invariants of the MSFP method.展开更多
The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton ...The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations （PDEs） derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations.展开更多
In this paper, we propose a variational integrator for nonlinear Schrodinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplect...In this paper, we propose a variational integrator for nonlinear Schrodinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrodinger equations with variable coefficients, cubic nonlinear Schrodinger equations and Gross-Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space.展开更多
Numerical dispersion relation of the multi-symplectic Runge-Kutta （MSRK） method for linear Hamiltonian PDEs is derived in the present paper, which is shown to be a discrete counterpart to that possessed by the diffe...Numerical dispersion relation of the multi-symplectic Runge-Kutta （MSRK） method for linear Hamiltonian PDEs is derived in the present paper, which is shown to be a discrete counterpart to that possessed by the differential equation. This provides further understanding of MSRK methods. However, much still remains to be investigated further.展开更多
In this paper, a multi-symplectic Hamiltonian formulation is presented for the coupled Schrdinger-Boussinesq equations （CSBE）. Then, a multi-symplectic scheme of the CSBE is derived. The discrete conservation laws o...In this paper, a multi-symplectic Hamiltonian formulation is presented for the coupled Schrdinger-Boussinesq equations （CSBE）. Then, a multi-symplectic scheme of the CSBE is derived. The discrete conservation laws of the Langmuir plasmon number and total perturbed number density are also proved. Numerical experiments show that the multi-symplectic scheme simulates the solitary waves for a long time, and preserves the conservation laws well.展开更多
We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can...We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem. For the linear subsystem, the multi-symplectic wavelet collocation method and the symplectic Euler method are employed in spatial and temporal discretization, respectively. For the nonlinear subsystem, the mid-point symplectic scheme is used. Numerical simulations show the effectiveness of the proposed method during long-time numerical calculation.展开更多
The multi-symplectic geometry for the GSDBM equation is presented in this paper. The multi-symplectic formulations for the GSDBM equation are presented and the local conservation laws are shown to correspond to certai...The multi-symplectic geometry for the GSDBM equation is presented in this paper. The multi-symplectic formulations for the GSDBM equation are presented and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is exemplified by the multisymplectic Preissmann scheme. The numerical experiments are given, and the results verify the efficiency of the Preissmann scheme.展开更多
文摘The multi-symplectic formulations of the 'Good' Boussinesq equation were considered. For the multi-symplectic formulation, a new fifteen-point difference scheme which is equivalent to the multi-symplectic Preissman integrator was derived. The numerical experiments show that, the multi- symplectic scheme have excellent long-time numerical. behavior.
文摘Aiming to solve the steering instability and hysteresis of agricultural robots in the process of movement,a fusion PID control method of particle swarm optimization(PSO)and genetic algorithm(GA)was proposed.The fusion algorithm took advantage of the fast optimization ability of PSO to optimize the population screening link of GA.The Simulink simulation results showed that the convergence of the fitness function of the fusion algorithm was accelerated,the system response adjustment time was reduced,and the overshoot was almost zero.Then the algorithm was applied to the steering test of agricultural robot in various scenes.After modeling the steering system of agricultural robot,the steering test results in the unloaded suspended state showed that the PID control based on fusion algorithm reduced the rise time,response adjustment time and overshoot of the system,and improved the response speed and stability of the system,compared with the artificial trial and error PID control and the PID control based on GA.The actual road steering test results showed that the PID control response rise time based on the fusion algorithm was the shortest,about 4.43 s.When the target pulse number was set to 100,the actual mean value in the steady-state regulation stage was about 102.9,which was the closest to the target value among the three control methods,and the overshoot was reduced at the same time.The steering test results under various scene states showed that the PID control based on the proposed fusion algorithm had good anti-interference ability,it can adapt to the changes of environment and load and improve the performance of the control system.It was effective in the steering control of agricultural robot.This method can provide a reference for the precise steering control of other robots.
基金National Key Research and Development Program of China,No.2023YFC3006704National Natural Science Foundation of China,No.42171047CAS-CSIRO Partnership Joint Project of 2024,No.177GJHZ2023097MI。
文摘Accurate prediction of flood events is important for flood control and risk management.Machine learning techniques contributed greatly to advances in flood predictions,and existing studies mainly focused on predicting flood resource variables using single or hybrid machine learning techniques.However,class-based flood predictions have rarely been investigated,which can aid in quickly diagnosing comprehensive flood characteristics and proposing targeted management strategies.This study proposed a prediction approach of flood regime metrics and event classes coupling machine learning algorithms with clustering-deduced membership degrees.Five algorithms were adopted for this exploration.Results showed that the class membership degrees accurately determined event classes with class hit rates up to 100%,compared with the four classes clustered from nine regime metrics.The nonlinear algorithms(Multiple Linear Regression,Random Forest,and least squares-Support Vector Machine)outperformed the linear techniques(Multiple Linear Regression and Stepwise Regression)in predicting flood regime metrics.The proposed approach well predicted flood event classes with average class hit rates of 66.0%-85.4%and 47.2%-76.0%in calibration and validation periods,respectively,particularly for the slow and late flood events.The predictive capability of the proposed prediction approach for flood regime metrics and classes was considerably stronger than that of hydrological modeling approach.
基金supported by the Research Project of China Southern Power Grid(No.056200KK52222031).
文摘This paper proposes an equivalent modeling method for photovoltaic(PV)power stations via a particle swarm optimization(PSO)K-means clustering(KMC)algorithm with passive filter parameter clustering to address the complexities,simulation time cost and convergence problems of detailed PV power station models.First,the amplitude–frequency curves of different filter parameters are analyzed.Based on the results,a grouping parameter set for characterizing the external filter characteristics is established.These parameters are further defined as clustering parameters.A single PV inverter model is then established as a prerequisite foundation.The proposed equivalent method combines the global search capability of PSO with the rapid convergence of KMC,effectively overcoming the tendency of KMC to become trapped in local optima.This approach enhances both clustering accuracy and numerical stability when determining equivalence for PV inverter units.Using the proposed clustering method,both a detailed PV power station model and an equivalent model are developed and compared.Simulation and hardwarein-loop(HIL)results based on the equivalent model verify that the equivalent method accurately represents the dynamic characteristics of PVpower stations and adapts well to different operating conditions.The proposed equivalent modeling method provides an effective analysis tool for future renewable energy integration research.
基金supported by the Major Science and Technology Programs in Henan Province(No.241100210100)Henan Provincial Science and Technology Research Project(No.252102211085,No.252102211105)+3 种基金Endogenous Security Cloud Network Convergence R&D Center(No.602431011PQ1)The Special Project for Research and Development in Key Areas of Guangdong Province(No.2021ZDZX1098)The Stabilization Support Program of Science,Technology and Innovation Commission of Shenzhen Municipality(No.20231128083944001)The Key scientific research projects of Henan higher education institutions(No.24A520042).
文摘Existing feature selection methods for intrusion detection systems in the Industrial Internet of Things often suffer from local optimality and high computational complexity.These challenges hinder traditional IDS from effectively extracting features while maintaining detection accuracy.This paper proposes an industrial Internet ofThings intrusion detection feature selection algorithm based on an improved whale optimization algorithm(GSLDWOA).The aim is to address the problems that feature selection algorithms under high-dimensional data are prone to,such as local optimality,long detection time,and reduced accuracy.First,the initial population’s diversity is increased using the Gaussian Mutation mechanism.Then,Non-linear Shrinking Factor balances global exploration and local development,avoiding premature convergence.Lastly,Variable-step Levy Flight operator and Dynamic Differential Evolution strategy are introduced to improve the algorithm’s search efficiency and convergence accuracy in highdimensional feature space.Experiments on the NSL-KDD and WUSTL-IIoT-2021 datasets demonstrate that the feature subset selected by GSLDWOA significantly improves detection performance.Compared to the traditional WOA algorithm,the detection rate and F1-score increased by 3.68%and 4.12%.On the WUSTL-IIoT-2021 dataset,accuracy,recall,and F1-score all exceed 99.9%.
基金the National Key Research and Development Program of China(Grant No.2022YFF0711400)which provided valuable financial support and resources for my research and made it possible for me to deeply explore the unknown mysteries in the field of lunar geologythe National Space Science Data Center Youth Open Project(Grant No.NSSDC2302001),which has not only facilitated the smooth progress of my research,but has also built a platform for me to communicate and cooperate with experts in the field.
文摘Impact craters are important for understanding the evolution of lunar geologic and surface erosion rates,among other functions.However,the morphological characteristics of these micro impact craters are not obvious and they are numerous,resulting in low detection accuracy by deep learning models.Therefore,we proposed a new multi-scale fusion crater detection algorithm(MSF-CDA)based on the YOLO11 to improve the accuracy of lunar impact crater detection,especially for small craters with a diameter of<1 km.Using the images taken by the LROC(Lunar Reconnaissance Orbiter Camera)at the Chang’e-4(CE-4)landing area,we constructed three separate datasets for craters with diameters of 0-70 m,70-140 m,and>140 m.We then trained three submodels separately with these three datasets.Additionally,we designed a slicing-amplifying-slicing strategy to enhance the ability to extract features from small craters.To handle redundant predictions,we proposed a new Non-Maximum Suppression with Area Filtering method to fuse the results in overlapping targets within the multi-scale submodels.Finally,our new MSF-CDA method achieved high detection performance,with the Precision,Recall,and F1 score having values of 0.991,0.987,and 0.989,respectively,perfectly addressing the problems induced by the lesser features and sample imbalance of small craters.Our MSF-CDA can provide strong data support for more in-depth study of the geological evolution of the lunar surface and finer geological age estimations.This strategy can also be used to detect other small objects with lesser features and sample imbalance problems.We detected approximately 500,000 impact craters in an area of approximately 214 km2 around the CE-4 landing area.By statistically analyzing the new data,we updated the distribution function of the number and diameter of impact craters.Finally,we identified the most suitable lighting conditions for detecting impact crater targets by analyzing the effect of different lighting conditions on the detection accuracy.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10572119, 10772147 and 10632030)the Doctoral Program Foundation of Education Ministry of China (Grant No 20070699028)+1 种基金the National Natural Science Foundation of Shaanxi Province of China (Grant No 2006A07)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment
文摘This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space. Recurring to the midpoint rule, it presents an implicit multi-symplectic scheme with discrete multi-symplectic conservation law to solve the partial differential equations which are derived from the generalized fifth-order KdV equation numerically. The results of the numerical experiments show that this multi-symplectic algorithm is good in accuracy and its long-time numerical behaviour is also perfect.
基金the National Natural Science Foundation of China(Nos.10632030 and 10572119)Program for New Century Excellent Talents of Ministry of Education of China(No.NCET-04-0958)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment
文摘In this paper, the multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space are considered. The complex method is introduced and a semi-implicit twenty-seven-points scheme with certain discrete conservation laws-a multi-symplectic conservation law （CLS）, a local energy conservation law （ECL） as well as a local momentum conservation law （MCL） --is constructed to discrete the PDEs that are derived from the membrane free vibration equation. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior,
基金Project supported by the National Natural Science Foundation of China(Nos.11161017,11071251,and 10871099)the National Basic Research Program of China(973 Program)(No.2007CB209603)+1 种基金the Natural Science Foundation of Hainan Province(No.110002)the Scientific Research Foun-dation of Hainan University(No.kyqd1053)
文摘Based on splitting multi-symplectic structures, a new multi-symplectic scheme is proposed and applied to a nonlinear wave equation. The explicit multi-symplectic scheme of the nonlinear wave equation is obtained, and the corresponding multi-symplectic conservation property is proved. The backward error analysis shows that the explicit multi-symplectic scheme has good accuracy. The sine-Gordon equation and the Klein-Gordon equation are simulated by an explicit multi-symplectic scheme. The numerical results show that the new explicit multi-symplectic scheme can well simulate the solitary wave behaviors of the nonlinear wave equation and approximately preserve the relative energy error of the equation.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10971226, 91130013, and 11001270)the National Basic Research Program of China (Grant No. 2009CB723802)
文摘We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov-Kuznetsov equation. The method combines the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler method for temporal discretization. It is verified that the proposed method has corresponding discrete multi-symplectic conservation laws. Numerical simulations indicate that the proposed scheme is characterized by excellent conservation.
基金supported by the National Natural Science Foundation of China (Nos. 10772147 and10632030)the Ph. D. Program Foundation of Ministry of Education of China (No. 20070699028)+2 种基金the Natural Science Foundation of Shaanxi Province of China (No. 2006A07)the Open Foundationof State Key Laboratory of Structural Analysis of Industrial Equipment (No. GZ0802)the Foundation for Fundamental Research of Northwestern Polytechnical University
文摘Nonlinear wave equations have been extensively investigated in the last sev- eral decades. The Landau-Ginzburg-Higgs equation, a typical nonlinear wave equation, is studied in this paper based on the multi-symplectic theory in the Hamilton space. The multi-symplectic Runge-Kutta method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the first-order partial differential equations （PDEs） derived from the Landau-Ginzburg-Higgs equation. The numerical re- sults for the soliton solution of the Landau-Ginzburg-Higgs equation are reported, showing that the multi-symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors.
基金Supported by the Natural Science Foundation of China under Grant No.0971226the 973 Project of China under Grant No.2009CB723802+1 种基金the Research Innovation Fund of Hunan Province under Grant No.CX2011B011the Innovation Fund of NUDT under Grant No.B110205
文摘Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.
基金Project supported by the Program for Innovative Research Team in Science and Technology in Fujian Province University,China,the Quanzhou High Level Talents Support Plan,China(Grant No.2017ZT012)the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Huaqiao University,China(Grant No.ZQN-YX502)
文摘A conformal multi-symplectic method has been proposed for the damped Korteweg–de Vries(DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissmann box scheme,we obtain a conformal multi-symplectic scheme for multi-symplectic partial differential equations(PDEs) with added dissipation. Applying it to the DKdV equation, we construct a conformal multi-symplectic algorithm for it, which is of second order accuracy in time. Numerical experiments demonstrate that the proposed method not only preserves the dissipation rate of mass exactly with periodic boundary conditions, but also has excellent long-time numerical behavior.
基金Project supported by the National Natural Science Foundation of China(Grant No.91130013)the Open Foundation of State Key Laboratory of High Performance Computing
文摘In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrtidinger-KdV equations （CS＇KE） with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral （MSFP） scheme for the CSKE. In numerical experiments, we compare the MSFP method with the Crank-Nicholson （CN） method. Our results show high accuracy, effectiveness, and good ability of conserving the invariants of the MSFP method.
基金Project supported by the National Natural Science Foundation of China (Nos.10572119,10772147,10632030)the Doctoral Program Foundation of Education Ministry of China (No.20070699028)+1 种基金the Natural Science Foundation of Shaanxi Province of China (No.2006A07)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment,Dalian University of Technology.
文摘The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations （PDEs） derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations.
基金supported by the National Natural Science Foundation of China(Grant No.11401259)the Fundamental Research Funds for the Central Universities,China(Grant No.JUSRR11407)
文摘In this paper, we propose a variational integrator for nonlinear Schrodinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrodinger equations with variable coefficients, cubic nonlinear Schrodinger equations and Gross-Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space.
基金The NNSF (10471054) of Chinathe China Postdoctoral Science Foundationthe Youth Foundation of Institute of Mathematics, Jilin University
文摘Numerical dispersion relation of the multi-symplectic Runge-Kutta （MSRK） method for linear Hamiltonian PDEs is derived in the present paper, which is shown to be a discrete counterpart to that possessed by the differential equation. This provides further understanding of MSRK methods. However, much still remains to be investigated further.
基金the National Natural Science Foundation of China(Grant Nos.11271171,11001072,and 11101381)Natural Science Foundation of Fujian Province,China(Grant No.2011J01010)+1 种基金the Fundamental Research Funds for the Central Universities,Chinathe Natural Science Foundation of Huaqiao University,China(Grant No.10QZR21)
文摘In this paper, a multi-symplectic Hamiltonian formulation is presented for the coupled Schrdinger-Boussinesq equations （CSBE）. Then, a multi-symplectic scheme of the CSBE is derived. The discrete conservation laws of the Langmuir plasmon number and total perturbed number density are also proved. Numerical experiments show that the multi-symplectic scheme simulates the solitary waves for a long time, and preserves the conservation laws well.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10971226,91130013,and 11001270)the National Basic Research Program of China(Grant No.2009CB723802)+1 种基金the Research Innovation Fund of Hunan Province,China (Grant No.CX2011B011)the Innovation Fund of National University of Defense Technology,China(Grant No.B120205)
文摘We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem. For the linear subsystem, the multi-symplectic wavelet collocation method and the symplectic Euler method are employed in spatial and temporal discretization, respectively. For the nonlinear subsystem, the mid-point symplectic scheme is used. Numerical simulations show the effectiveness of the proposed method during long-time numerical calculation.
基金Supported by the Differential Equation Innovation Team(CXTD003,2013XYZ19)
文摘The multi-symplectic geometry for the GSDBM equation is presented in this paper. The multi-symplectic formulations for the GSDBM equation are presented and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is exemplified by the multisymplectic Preissmann scheme. The numerical experiments are given, and the results verify the efficiency of the Preissmann scheme.
