An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditio...An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditions and their convergence are studied. The two-step continuity Runge-Kutta methods possess good numerical stability properties and higher stage-order, and keep the explicit process of computing the Runge-Kutta stages. The numerical experiments show that the TSCRK methods are efficient.展开更多
This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solutio...This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.展开更多
There are the application scope limits for single differential-mode current injection test method, so in order to carry out injection susceptibility test for two-pieces equipment interconnected with both ends of a cab...There are the application scope limits for single differential-mode current injection test method, so in order to carry out injection susceptibility test for two-pieces equipment interconnected with both ends of a cable simultaneously, a double differential-mode current in- jection test method (DDMCI) is proposed. The method adopted the equivalence source wave theorem and Baum-Liu-Tesche(BLT) equation as its theory foundation. The equivalent corresponding relation between injection voltage and radiation electric field intensity is derived, and the phase relation between the two injection voltage sources is confirmed. The results indicate that the amplitude and phase of the equivalent injection voltage source is closely related to the S parameter of directional coupling device, the transmission line length, and the source vector in BLT equation, but has nothing to do with the reflection coefficient between the two equipment pieces. Therefore, by choosing the right amplitude and phase of the double injection voltage sources, the DDMCI test is equivalent to the radiation test for two interconnected equipment of a system.展开更多
A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such m...A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such methods.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 differential cubature solution to the problem of a Mindlin plate lying on the Winkler foundation with two simply supported edges and two clamped edges was derived.Discrete numerical technology and shape functions ...The differential cubature solution to the problem of a Mindlin plate lying on the Winkler foundation with two simply supported edges and two clamped edges was derived.Discrete numerical technology and shape functions were used to ensure that the solution is suitable to irregular shaped plates.Then,the mechanical model and the solution were employed to model the protection layer that isolates the mining stopes from sea water in Sanshandao gold mine,which is the first subsea mine of China.Furthermore,thickness optimizations for the protection layers above each stope were conducted based on the maximum principle stress criterion,and the linear relations between the best protection layer thickness and the stope area under different safety factors were regressed to guide the isolation design.The method presented in this work provides a practical way to quickly design the isolation layer thickness in subsea mining.展开更多
Top structure and basement will confront the risk of being damaged on account of large stress and strain fields incurred by differential uplift and settlement between inner column and diaphragm wall in top-down method...Top structure and basement will confront the risk of being damaged on account of large stress and strain fields incurred by differential uplift and settlement between inner column and diaphragm wall in top-down method. Top-down excavation of the Metro Line 10 in Shanghai was modeled with finite element analysis software ABAQUS and parameters of subsoil were obtained by inverse analysis. Based on the finite element model and parameters, changes in the following factors were made to find more effective methods to restrain differential uplift and settlement: length of diaphragm wall, thickness of jet-grouting reinforcement layer, ways of subsoil reinforcement, sequence of pit excavation, connection between slabs and diaphragm wall or column and width of pit. Several significant results are acquired. The longer the diaphragm wall is, the greater the differential uplift between column and diaphragm wall is. Rigidity of roof slab is in general not strong enough to keep diaphragm wall and column undergoing the same uplift during excavation; Uplift at head of column and differential uplift between column and diaphragm wall decrease when subsoil from-16.6 to-43 m in pit is reinforced through jet-grouting. But, as excavation proceeds to a lower level, benefit from soil reinforcement diminishes. During the process applying vertical load, the larger the depth of diaphragm wall is, the smaller the settlement is at head of column and diaphragm wall, and the greater the differential settlement is between column and diaphragm wall. When friction connection is implemented between column, diaphragm wall and floor slabs, uplifts at head of column and diaphragm wall are larger than those of the case when tie connection is implemented, and so does differential uplift between column and diaphragm wall. The maximum deflection of diaphragm wall decreases by 58% on account of soil reinforcement in pit. The maximum deflection of diaphragm wall decreases by 61.2% when friction connection is implemented instead of tie connection.展开更多
A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forc...A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.展开更多
Monotone sequences are constructed that converge to the ex tremal solutions of second order three point boundary value problems when the functions involved do not possess any monotone properties.
In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic ...In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method for avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given.展开更多
文摘An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditions and their convergence are studied. The two-step continuity Runge-Kutta methods possess good numerical stability properties and higher stage-order, and keep the explicit process of computing the Runge-Kutta stages. The numerical experiments show that the TSCRK methods are efficient.
文摘This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.
基金Project supported by Arm Pre-research Program （51333040101）, National Defense 973 Program （6131380301 ）, National Natural Science Foundation of China （61040003）.
文摘There are the application scope limits for single differential-mode current injection test method, so in order to carry out injection susceptibility test for two-pieces equipment interconnected with both ends of a cable simultaneously, a double differential-mode current in- jection test method (DDMCI) is proposed. The method adopted the equivalence source wave theorem and Baum-Liu-Tesche(BLT) equation as its theory foundation. The equivalent corresponding relation between injection voltage and radiation electric field intensity is derived, and the phase relation between the two injection voltage sources is confirmed. The results indicate that the amplitude and phase of the equivalent injection voltage source is closely related to the S parameter of directional coupling device, the transmission line length, and the source vector in BLT equation, but has nothing to do with the reflection coefficient between the two equipment pieces. Therefore, by choosing the right amplitude and phase of the double injection voltage sources, the DDMCI test is equivalent to the radiation test for two interconnected equipment of a system.
文摘A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such methods.
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Projects(51504044,51204100)supported by National Natural Science Foundation of ChinaProject(14KF05)supported by the Research Fund of The State Key Laboratory of Coal Resources and Mine Safety,CUMT,China+3 种基金Project(cstc2016jcyj A1861)supported by the Research Fund of Chongqing Basic Science and Cutting-Edge Technology Special Projects,ChinaProject(2015CDJXY)supported by the Fundamental Research Funds for the Central UniversitiesProject supported by the China Postdoctoral Science FoundationProject(2011DA105287-MS201503)supported by the Independent Subject of State Key Laboratory of Coal Mine Disaster Dynamics and Control,China
文摘The differential cubature solution to the problem of a Mindlin plate lying on the Winkler foundation with two simply supported edges and two clamped edges was derived.Discrete numerical technology and shape functions were used to ensure that the solution is suitable to irregular shaped plates.Then,the mechanical model and the solution were employed to model the protection layer that isolates the mining stopes from sea water in Sanshandao gold mine,which is the first subsea mine of China.Furthermore,thickness optimizations for the protection layers above each stope were conducted based on the maximum principle stress criterion,and the linear relations between the best protection layer thickness and the stope area under different safety factors were regressed to guide the isolation design.The method presented in this work provides a practical way to quickly design the isolation layer thickness in subsea mining.
基金Projects(51208071,51108312) supported by the National Natural Science Foundation of China
文摘Top structure and basement will confront the risk of being damaged on account of large stress and strain fields incurred by differential uplift and settlement between inner column and diaphragm wall in top-down method. Top-down excavation of the Metro Line 10 in Shanghai was modeled with finite element analysis software ABAQUS and parameters of subsoil were obtained by inverse analysis. Based on the finite element model and parameters, changes in the following factors were made to find more effective methods to restrain differential uplift and settlement: length of diaphragm wall, thickness of jet-grouting reinforcement layer, ways of subsoil reinforcement, sequence of pit excavation, connection between slabs and diaphragm wall or column and width of pit. Several significant results are acquired. The longer the diaphragm wall is, the greater the differential uplift between column and diaphragm wall is. Rigidity of roof slab is in general not strong enough to keep diaphragm wall and column undergoing the same uplift during excavation; Uplift at head of column and differential uplift between column and diaphragm wall decrease when subsoil from-16.6 to-43 m in pit is reinforced through jet-grouting. But, as excavation proceeds to a lower level, benefit from soil reinforcement diminishes. During the process applying vertical load, the larger the depth of diaphragm wall is, the smaller the settlement is at head of column and diaphragm wall, and the greater the differential settlement is between column and diaphragm wall. When friction connection is implemented between column, diaphragm wall and floor slabs, uplifts at head of column and diaphragm wall are larger than those of the case when tie connection is implemented, and so does differential uplift between column and diaphragm wall. The maximum deflection of diaphragm wall decreases by 58% on account of soil reinforcement in pit. The maximum deflection of diaphragm wall decreases by 61.2% when friction connection is implemented instead of tie connection.
基金supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)the Fundamental Research Funds for the Central Universities(K50511700004)
文摘A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.
文摘Monotone sequences are constructed that converge to the ex tremal solutions of second order three point boundary value problems when the functions involved do not possess any monotone properties.
基金The project was supported by the National Natural Science Faundation of China
文摘In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method for avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given.
