In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is an...In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is analyzed, and the reason why conjugate gradient iteration is not a good relaxation scheme for multi-grid algorithm is explored. The numerical results show that our algebraic block Gauss Seidel multi-grid algorithm is very effective.展开更多
The aim of the paper is to solve the problem of over-segmentation problem generated by Watershed segmentation algorithm or unstable clarity judgment by small areas in image fusion. A multi-focus image fusion algorithm...The aim of the paper is to solve the problem of over-segmentation problem generated by Watershed segmentation algorithm or unstable clarity judgment by small areas in image fusion. A multi-focus image fusion algorithm is proposed based on CNN segmentation and algebraic multi-grid method (CNN-AMG). Firstly, the CNN segmentation result was utilized to instruct the merging process of the regions generated by the Watershed segmentation method. Then the clear regions were selected into the temporary fusion image and the final fusion process was performed according to the clarity evaluation index, which was computed with the algebraic multi-grid method (AMG). The experimental results show that the fused image quality obtained by the CNNAMG algorithm outperforms the traditional fusion methods such as DSIFT fusion method, CNN fusion method, ASR fusion method, GFF fusion method and so on with some evaluation indexes.展开更多
Aimed at the demand of contingency return at any time during the near-moon phase in the manned lunar landing missions,a fast calculation method for three-impulse contingency return trajectories is proposed.Firstly,a t...Aimed at the demand of contingency return at any time during the near-moon phase in the manned lunar landing missions,a fast calculation method for three-impulse contingency return trajectories is proposed.Firstly,a three-impulse contingency return trajectory scheme is presented by combining the Lambert transfer and maneuver at the special point.Secondly,a calculation model of three-impulse contingency return trajectories is established.Then,fast calculation methods are proposed by adopting the high-order Taylor expansion of differential algebra in the twobody trajectory dynamics model and perturbed trajectory dynamics model.Finally,the performance of the proposed methods is verified by numerical simulation.The results indicate that the fast calculation method of two-body trajectory has higher calculation efficiency compared to the semi-analytical calculation method under a certain accuracy condition.Due to its high efficiency,the characteristics of the three-impulse contingency return trajectories under different contingency scenarios are further analyzed expeditiously.These findings can be used for the design of contingency return trajectories in future manned lunar landing missions.展开更多
An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential e...An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential equationwhich is regarded as an extended elliptic equation and whose degree Υ is expanded to the case of r>4.The efficiency ofthe method is demonstrated by the KdV equation and the variant Boussinesq equations.The results indicate that themethod not only offers all solutions obtained by using Fu's and Fan's methods,but also some new solutions.展开更多
This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. ...This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.展开更多
The algebraic energy method （AEM） is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states： a^3∑＋ state of NaK, X^2∑＋ state of XeBr, X^2∑＋ state of HgI, X^1...The algebraic energy method （AEM） is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states： a^3∑＋ state of NaK, X^2∑＋ state of XeBr, X^2∑＋ state of HgI, X^1∑＋ state of LiH, A3∏（1） state of IC1, X^1∑＋ state of CsH, A（3∏1） and B0＋（3∏） states of CIF, 21∏ state of KRb, X^1∑＋ state of CO, and c^3∑＋ state of NaK molecule. The results show that the values of De computed by using the AEM are satisfactorily accurate compared with experimental ones. The AEM can serve as an economic and useful tool to generate a reliable De within an allowed experimental error for the electronic states whose molecular dissociation energies are unavailable from the existing literature展开更多
The algebraic collapsing acceleration(ACA)technique maximizes the use of geometric flexibility of the method of characteristics(MOC).The spatial grids for loworder ACA are the same as the high-order transport,which ma...The algebraic collapsing acceleration(ACA)technique maximizes the use of geometric flexibility of the method of characteristics(MOC).The spatial grids for loworder ACA are the same as the high-order transport,which makes the numerical solution of ACA equations costly,especially for large-size problems.To speed-up the MOC transport iterations effectively for general geometry,a coarse-mesh ACA method that involves selectively merging fine-mesh cells with identical materials,called material-mesh ACA(MMACA),is presented.The energy group batching(EGB)strategy in the tracing process is proposed to increase the parallel efficiency for microscopic crosssection problems.Microscopic and macroscopic crosssection benchmark problems are used to validate and analyse the accuracy and efficiency of the MMACA method.The maximum errors in the multiplication factor and pin power distributions are from the VERA-4 B-2 D case with silver-indium-cadmium(AIC)control rods inserted and are 104 pcm and 1.97%,respectively.Compared with the single-thread ACA solution,the maximum speed-up ratio reached 25 on 12 CPU cores for microscopic cross-section VERA-4-2 D problem.For the C5 G7-2 D and LRA-2 D benchmarks,the MMACA method can reduce the computation time by approximately one half.The present work proposes the MMACA method and demonstrates its ability to effectively accelerate MOC transport iterations.展开更多
To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots(CSPRs),point-to-point trajectory planning demands an und...To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots(CSPRs),point-to-point trajectory planning demands an under-constrained cable-suspended parallel robot(UCPR)with variable angle and height cable mast as described in this paper.The end-effector of the UCPR with three cables can achieve three translational degrees of freedom(DOFs).The inverse kinematic and dynamic modeling of the UCPR considering the angle and height of cable mast are completed.The motion trajectory of the end-effector comprising six segments is given.The connection points of the trajectory segments(except for point P3 in the X direction)are devised to have zero instantaneous velocities,which ensure that the acceleration has continuity and the planned acceleration curve achieves smooth transition.The trajectory is respectively planned using three algebraic methods,including fifth degree polynomial,cycloid trajectory,and double-S velocity curve.The results indicate that the trajectory planned by fifth degree polynomial method is much closer to the given trajectory of the end-effector.Numerical simulation and experiments are accomplished for the given trajectory based on fifth degree polynomial planning.At the points where the velocity suddenly changes,the length and tension variation curves of the planned and unplanned three cables are compared and analyzed.The OptiTrack motion capture system is adopted to track the end-effector of the UCPR during the experiment.The effectiveness and feasibility of fifth degree polynomial planning are validated.展开更多
This is a study of the Durand-Kerner and Nourein methods for finding the roots of a given algebraic equation simultaneously. We consider the conditions under which the iterative methods fail. The numerical example is ...This is a study of the Durand-Kerner and Nourein methods for finding the roots of a given algebraic equation simultaneously. We consider the conditions under which the iterative methods fail. The numerical example is presented.展开更多
Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending ext...Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending external field. For this system, the property of the concurrence that is only dependent on the coupling constant J and total values of the external field is proved. Furthermore, we found that the thermal concurrence of the system under a static random external field is a function of the coupling constant J, temperature T, and the magnitude of external field.展开更多
An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byu...An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.展开更多
A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, th...A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.展开更多
The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal de...The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal development method of algebraic and numerical algorithms. The method implements the complete refinement process from abstract specifications to a concrete executable program. It uses the core idea of partition and recursion for formal derivation and combines the mathematical induction based on strict mathematical logic with Hoare axiom for correctness verification. This development method converts creative work into non-creative work as much as possible while ensuring the correctness of the algorithm, which can not only verify the correctness of the existing algebraic and numerical algorithms but also guide the development of efficient unknown algorithms for such problems. This paper takes the non-recursive implementation of the Extended Euclidean Algorithm and Horner's method as examples. Therefore, the effectiveness and feasibility of this method are further verified.展开更多
In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study...In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study show that by applying the new direct algebraic method to the pKP equation,the behavior of the obliquely interacting surface waves in two dimensions can be analyzed.This article fairly clarifies the behaviors of surface waves in shallow waters.In the literature,several mathematical models have been developed in attempt to study these behaviors,with nonlinear mathematics being one of the most important steps;however,the investigations are still at a level that can be called‘baby steps’.Therefore,every study to be carried out in this context is of great importance.Thus,this study will serve as a reference to guide scientists working in this field.展开更多
A class of parallel Rosenbrock methods for differential algebraic equations are presented in this paper. The local truncation errors are defined and the order conditions are established by using the DA-trees and DA-se...A class of parallel Rosenbrock methods for differential algebraic equations are presented in this paper. The local truncation errors are defined and the order conditions are established by using the DA-trees and DA-series. The paper also deals with the convergence of the parallel Rosenbrock methods for h -> 0 and states the bounds for the global errors of the methods. Some particular methods are obtained by solving the order equations and a numerical example is given, from which the theoretical orders are actually observed.展开更多
The algebraic structure and the Poisson method for a weakly nonholonomic system are studied.The differential equations of motion of the system can be written in a contravariant algebra form and its algebraic structure...The algebraic structure and the Poisson method for a weakly nonholonomic system are studied.The differential equations of motion of the system can be written in a contravariant algebra form and its algebraic structure is discussed.The Poisson theory for the systems which possess Lie algebra structure is generalized to the weakly nonholonomic system.An example is given to illustrate the application of the result.展开更多
A class of parallel multisplitting AOR method for solving large scale system of nonlinear equations A φ(x)+Bψ(x)=b was proposed. Under certain conditions, the existence and uniqueness of the solution of this system ...A class of parallel multisplitting AOR method for solving large scale system of nonlinear equations A φ(x)+Bψ(x)=b was proposed. Under certain conditions, the existence and uniqueness of the solution of this system of nonlinear equations were proved, and the global convergence theory of the new method was set up.展开更多
An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byu...An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.展开更多
A series of sufficient and necessary conditions for the algebraic stability of multistepRunge-Kutta methods is obtained, most of which can be regarded as extension of the relevant results available for Runge-Kutta met...A series of sufficient and necessary conditions for the algebraic stability of multistepRunge-Kutta methods is obtained, most of which can be regarded as extension of the relevant results available for Runge-Kutta methods, especially, for Radau Ⅰ A, Radau Ⅱ A and Gaussian Runge-Kutta methods.展开更多
We propose a continuous analogy of Newton’s method with inner iteration for solving a system of linear algebraic equations. Implementation of inner iterations is carried out in two ways. The former is to fix the numb...We propose a continuous analogy of Newton’s method with inner iteration for solving a system of linear algebraic equations. Implementation of inner iterations is carried out in two ways. The former is to fix the number of inner iterations in advance. The latter is to use the inexact Newton method for solution of the linear system of equations that arises at each stage of outer iterations. We give some new choices of iteration parameter and of forcing term, that ensure the convergence of iterations. The performance and efficiency of the proposed iteration is illustrated by numerical examples that represent a wide range of typical systems.展开更多
基金Supported by the Natlonal Natural Science Foundation of China
文摘In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is analyzed, and the reason why conjugate gradient iteration is not a good relaxation scheme for multi-grid algorithm is explored. The numerical results show that our algebraic block Gauss Seidel multi-grid algorithm is very effective.
文摘The aim of the paper is to solve the problem of over-segmentation problem generated by Watershed segmentation algorithm or unstable clarity judgment by small areas in image fusion. A multi-focus image fusion algorithm is proposed based on CNN segmentation and algebraic multi-grid method (CNN-AMG). Firstly, the CNN segmentation result was utilized to instruct the merging process of the regions generated by the Watershed segmentation method. Then the clear regions were selected into the temporary fusion image and the final fusion process was performed according to the clarity evaluation index, which was computed with the algebraic multi-grid method (AMG). The experimental results show that the fused image quality obtained by the CNNAMG algorithm outperforms the traditional fusion methods such as DSIFT fusion method, CNN fusion method, ASR fusion method, GFF fusion method and so on with some evaluation indexes.
基金co-supported by the National Natural Science Foundation of China(No.12072365)the Technology Innovation Team of Manned Space Engineering,China。
文摘Aimed at the demand of contingency return at any time during the near-moon phase in the manned lunar landing missions,a fast calculation method for three-impulse contingency return trajectories is proposed.Firstly,a three-impulse contingency return trajectory scheme is presented by combining the Lambert transfer and maneuver at the special point.Secondly,a calculation model of three-impulse contingency return trajectories is established.Then,fast calculation methods are proposed by adopting the high-order Taylor expansion of differential algebra in the twobody trajectory dynamics model and perturbed trajectory dynamics model.Finally,the performance of the proposed methods is verified by numerical simulation.The results indicate that the fast calculation method of two-body trajectory has higher calculation efficiency compared to the semi-analytical calculation method under a certain accuracy condition.Due to its high efficiency,the characteristics of the three-impulse contingency return trajectories under different contingency scenarios are further analyzed expeditiously.These findings can be used for the design of contingency return trajectories in future manned lunar landing missions.
基金National Natural Science Foundation of China under Grant No.10672053
文摘An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential equationwhich is regarded as an extended elliptic equation and whose degree Υ is expanded to the case of r>4.The efficiency ofthe method is demonstrated by the KdV equation and the variant Boussinesq equations.The results indicate that themethod not only offers all solutions obtained by using Fu's and Fan's methods,but also some new solutions.
文摘This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.
基金Project supported by the Science Foundation of China West Normal University （Grant No 05B016） and the Science Foundation of Sichuan province Educational Bureau of China （Grant No 2006A080）.
文摘The algebraic energy method （AEM） is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states： a^3∑＋ state of NaK, X^2∑＋ state of XeBr, X^2∑＋ state of HgI, X^1∑＋ state of LiH, A3∏（1） state of IC1, X^1∑＋ state of CsH, A（3∏1） and B0＋（3∏） states of CIF, 21∏ state of KRb, X^1∑＋ state of CO, and c^3∑＋ state of NaK molecule. The results show that the values of De computed by using the AEM are satisfactorily accurate compared with experimental ones. The AEM can serve as an economic and useful tool to generate a reliable De within an allowed experimental error for the electronic states whose molecular dissociation energies are unavailable from the existing literature
基金supported by the Chinese TMSR Strategic Pioneer Science and Technology Project(No.XDA02010000)the Frontier Science Key Program of the Chinese Academy of Sciences(No.QYZDY-SSW-JSC016)。
文摘The algebraic collapsing acceleration(ACA)technique maximizes the use of geometric flexibility of the method of characteristics(MOC).The spatial grids for loworder ACA are the same as the high-order transport,which makes the numerical solution of ACA equations costly,especially for large-size problems.To speed-up the MOC transport iterations effectively for general geometry,a coarse-mesh ACA method that involves selectively merging fine-mesh cells with identical materials,called material-mesh ACA(MMACA),is presented.The energy group batching(EGB)strategy in the tracing process is proposed to increase the parallel efficiency for microscopic crosssection problems.Microscopic and macroscopic crosssection benchmark problems are used to validate and analyse the accuracy and efficiency of the MMACA method.The maximum errors in the multiplication factor and pin power distributions are from the VERA-4 B-2 D case with silver-indium-cadmium(AIC)control rods inserted and are 104 pcm and 1.97%,respectively.Compared with the single-thread ACA solution,the maximum speed-up ratio reached 25 on 12 CPU cores for microscopic cross-section VERA-4-2 D problem.For the C5 G7-2 D and LRA-2 D benchmarks,the MMACA method can reduce the computation time by approximately one half.The present work proposes the MMACA method and demonstrates its ability to effectively accelerate MOC transport iterations.
基金National Natural Science Foundation of China(Grant Nos.51925502,51575150).
文摘To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots(CSPRs),point-to-point trajectory planning demands an under-constrained cable-suspended parallel robot(UCPR)with variable angle and height cable mast as described in this paper.The end-effector of the UCPR with three cables can achieve three translational degrees of freedom(DOFs).The inverse kinematic and dynamic modeling of the UCPR considering the angle and height of cable mast are completed.The motion trajectory of the end-effector comprising six segments is given.The connection points of the trajectory segments(except for point P3 in the X direction)are devised to have zero instantaneous velocities,which ensure that the acceleration has continuity and the planned acceleration curve achieves smooth transition.The trajectory is respectively planned using three algebraic methods,including fifth degree polynomial,cycloid trajectory,and double-S velocity curve.The results indicate that the trajectory planned by fifth degree polynomial method is much closer to the given trajectory of the end-effector.Numerical simulation and experiments are accomplished for the given trajectory based on fifth degree polynomial planning.At the points where the velocity suddenly changes,the length and tension variation curves of the planned and unplanned three cables are compared and analyzed.The OptiTrack motion capture system is adopted to track the end-effector of the UCPR during the experiment.The effectiveness and feasibility of fifth degree polynomial planning are validated.
文摘This is a study of the Durand-Kerner and Nourein methods for finding the roots of a given algebraic equation simultaneously. We consider the conditions under which the iterative methods fail. The numerical example is presented.
文摘Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending external field. For this system, the property of the concurrence that is only dependent on the coupling constant J and total values of the external field is proved. Furthermore, we found that the thermal concurrence of the system under a static random external field is a function of the coupling constant J, temperature T, and the magnitude of external field.
文摘An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.
文摘A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.
基金Supported by the National Natural Science Foundation of China (61862033, 61762049, 61902162)Jiangxi Provincial Natural Science Foundation (20202BABL202026, 20202BABL202025, 20202BAB202015)。
文摘The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal development method of algebraic and numerical algorithms. The method implements the complete refinement process from abstract specifications to a concrete executable program. It uses the core idea of partition and recursion for formal derivation and combines the mathematical induction based on strict mathematical logic with Hoare axiom for correctness verification. This development method converts creative work into non-creative work as much as possible while ensuring the correctness of the algorithm, which can not only verify the correctness of the existing algebraic and numerical algorithms but also guide the development of efficient unknown algorithms for such problems. This paper takes the non-recursive implementation of the Extended Euclidean Algorithm and Horner's method as examples. Therefore, the effectiveness and feasibility of this method are further verified.
文摘In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study show that by applying the new direct algebraic method to the pKP equation,the behavior of the obliquely interacting surface waves in two dimensions can be analyzed.This article fairly clarifies the behaviors of surface waves in shallow waters.In the literature,several mathematical models have been developed in attempt to study these behaviors,with nonlinear mathematics being one of the most important steps;however,the investigations are still at a level that can be called‘baby steps’.Therefore,every study to be carried out in this context is of great importance.Thus,this study will serve as a reference to guide scientists working in this field.
基金the National Natural Science Foundation of China (No. 19871080)
文摘A class of parallel Rosenbrock methods for differential algebraic equations are presented in this paper. The local truncation errors are defined and the order conditions are established by using the DA-trees and DA-series. The paper also deals with the convergence of the parallel Rosenbrock methods for h -> 0 and states the bounds for the global errors of the methods. Some particular methods are obtained by solving the order equations and a numerical example is given, from which the theoretical orders are actually observed.
基金supported by the National Natural Science Foundation of China(10772025,10932002,10972031)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics
文摘The algebraic structure and the Poisson method for a weakly nonholonomic system are studied.The differential equations of motion of the system can be written in a contravariant algebra form and its algebraic structure is discussed.The Poisson theory for the systems which possess Lie algebra structure is generalized to the weakly nonholonomic system.An example is given to illustrate the application of the result.
文摘A class of parallel multisplitting AOR method for solving large scale system of nonlinear equations A φ(x)+Bψ(x)=b was proposed. Under certain conditions, the existence and uniqueness of the solution of this system of nonlinear equations were proved, and the global convergence theory of the new method was set up.
文摘An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.
文摘A series of sufficient and necessary conditions for the algebraic stability of multistepRunge-Kutta methods is obtained, most of which can be regarded as extension of the relevant results available for Runge-Kutta methods, especially, for Radau Ⅰ A, Radau Ⅱ A and Gaussian Runge-Kutta methods.
文摘We propose a continuous analogy of Newton’s method with inner iteration for solving a system of linear algebraic equations. Implementation of inner iterations is carried out in two ways. The former is to fix the number of inner iterations in advance. The latter is to use the inexact Newton method for solution of the linear system of equations that arises at each stage of outer iterations. We give some new choices of iteration parameter and of forcing term, that ensure the convergence of iterations. The performance and efficiency of the proposed iteration is illustrated by numerical examples that represent a wide range of typical systems.
