In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
The stability of the tunnel portal slope is crucial for ensuring safe tunnel construction.Thus,a sound stability evaluation is of significance.Given the unique geological characteristics of tunnel portal slopes,it is ...The stability of the tunnel portal slope is crucial for ensuring safe tunnel construction.Thus,a sound stability evaluation is of significance.Given the unique geological characteristics of tunnel portal slopes,it is necessary to establish a specific evaluation indicator system that differs from those used for ordinary slopes.Based on the unascertained measure method,uncertainties in the indicator are addressed by introducing the left and right half cloud asymmetric cloud model to optimize the linear membership function.The subjectivity of confidence criterion level identification is also improved by using the Euclidean distance method.Thus,a stability evaluation model for the tunnel portal slope is established based on the improved unascertained measure method.Finally,using the collected tunnel portal slope data,the results of four evaluation methods are compared with the safety factor levels.The evaluation methods include the traditional unascertained measure method,the method improved by using the left and right half cloud asymmetric cloud model,the method improved by using the Euclidean distance method,and the method improved by using both the left and right half cloud asymmetric cloud model and the Euclidean distance method.The results show that the accuracy rates of these four methods are 50%,55%,85%,and 90%,respectively.Among them,the joint improvement method has the slightest deviation,with only one level,while the other three methods had deviations of two levels.This result verifies the stability and effectiveness of the joint improvement method,providing a reference for tunnel portal slope stability evaluation.展开更多
Alternating direction implicit (A.D.I.) schemes have been proved valuable in the approximation of the solutions of parabolic partial differential equations in multi-dimensional space. Consider equations in the form pa...Alternating direction implicit (A.D.I.) schemes have been proved valuable in the approximation of the solutions of parabolic partial differential equations in multi-dimensional space. Consider equations in the form partial derivative u/partial derivative t - partial derivative/partial derivative x(a(x,y,t) partial derivative u/partial derivative x) - partial derivative/partial derivative y(b(x,y,t) partial derivative u partial derivative y) = f Two A.D.I. schemes, Peaceman-Rachford scheme and Douglas scheme will be studied. In the literature, stability and convergence have been analysed with Fourier Method, which cannot be extended beyond the model problem with constant coefficients. Additionally, L-2 energy method has been introduced to analyse the case of non-constant coefficients, however, the conclusions are too weak and incomplete because of the so-called 'equivalence between L-2 norm and H-1 semi-norm'. In this paper, we try to improve these conclusions by H-1 energy estimating method. The principal results are that both of the two A.D.I. schemes are absolutely stable and converge to the exact solution with error estimations O(Delta t(2) + h(2)) in discrete H-1 norm. This implies essential improvement of existing conclusions.展开更多
The study of artificial slope stability has been a key item of geological engineering projects. Though more evaluation methods are available,result of stability evaluation simulation does not explain the actual proble...The study of artificial slope stability has been a key item of geological engineering projects. Though more evaluation methods are available,result of stability evaluation simulation does not explain the actual problem owing to the diversified geological engineering factors and complexity. The author made a detailed study based on surveys of large amount of geological engineering research on Donggang Power Plant slope project,discussed the comprehensive factors influencing the project,and gave analytical calculation and evaluation to the improved response surface of the slope project. The study result shows that the slope is stable,which can provide scientific basis for designing the slope.展开更多
This paper deals with the mean-square exponential input-to-state stability(exp-ISS)of Euler-Maruyama(EM)method applied to stochastic control systems(SCSs).The aim is to find out the conditions of the exact and EM meth...This paper deals with the mean-square exponential input-to-state stability(exp-ISS)of Euler-Maruyama(EM)method applied to stochastic control systems(SCSs).The aim is to find out the conditions of the exact and EM method solutions to an SCS having the property of mean-square exp-ISS without involving control Lyapunov functions.Second moment boundedness and an appropriate form of strong convergence are achieved under global Lipschitz coeffcients and mean-square continuous random inputs.Under the strong convergent condition,it is shown that the mean-square exp-ISS of an SCS holds if and only if that of the EM method is preserved for suffciently small step size.展开更多
Presents information on a study which dealt with the error behavior and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation as applied to the nonlinear delay differential eq...Presents information on a study which dealt with the error behavior and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation as applied to the nonlinear delay differential equations. Methods and the basic lemmas; Analysis of convergence and stability.展开更多
In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been...In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of thecharacteristics of a control dynamics system on its measured procedure will simplify thedecision method of movement stability problems.展开更多
Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach space.To break through the ...Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach space.To break through the order barrier p≤1 of unconditionally contractive linear multistep methods for dissipative systems,strongly dissipative systems are introduced.By employing the error growth function of the methods,new contractivity and convergence results of stepsize-dependent linear multistep methods on infinite integration intervals are provided for strictly dissipative systems(ω<0)and strongly dissipative systems.Some applications of the main results to several linear multistep methods,including the trapezoidal rule,are supplied.The theoretical results are also illustrated by a set of numerical experiments.展开更多
In this paper,we investigate the theoretical and numerical analysis of the stochastic Volterra integro-differential equations(SVIDEs)driven by L´evy noise.The existence,uniqueness,boundedness and mean square expo...In this paper,we investigate the theoretical and numerical analysis of the stochastic Volterra integro-differential equations(SVIDEs)driven by L´evy noise.The existence,uniqueness,boundedness and mean square exponential stability of the analytic solutions for SVIDEs driven by L´evy noise are considered.The split-step theta method of SVIDEs driven by L´evy noise is proposed.The boundedness of the numerical solution and strong convergence are proved.Moreover,its mean square exponential stability is obtained.Some numerical examples are given to support the theoretical results.展开更多
In this paper,numerical methods for the time-changed stochastic differential equations of the form dY(t)=a(Y(t))dt+b(Y(t))dE(t)+s(Y(t))dB(E(t))are investigated,where all the coefficients a(·),b(·)and s(·...In this paper,numerical methods for the time-changed stochastic differential equations of the form dY(t)=a(Y(t))dt+b(Y(t))dE(t)+s(Y(t))dB(E(t))are investigated,where all the coefficients a(·),b(·)and s(·)are allowed to contain some super-linearly growing terms.An explicit method is proposed by using the idea of truncating terms that grow too fast.Strong convergence in the finite time of the proposed method is proved and the convergence rate is obtained.The proposed method is also proved to be able to reproduce the asymptotic stability of the underlying equation in the almost sure sense.Simulations are provided to demonstrate the theoretical results.展开更多
A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further c...A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further confirmed by some numerical experiments.Especially, the numerical method and its theories can be applied to specialcases, such as delay differential-algebraic equations and integral differential-algebraicequations.展开更多
This paper presents a comprehensive numerical study of the two-dimensional time-dependent heat conduction equation using the Forward Time Centered Space(FTCS)finite difference scheme.The heat equation is a fundamental...This paper presents a comprehensive numerical study of the two-dimensional time-dependent heat conduction equation using the Forward Time Centered Space(FTCS)finite difference scheme.The heat equation is a fundamental parabolic partial differential equation,models the diffusion of thermal energy in a medium and is applicable in areas such as thermal insulation design,mi-crochip cooling,and biological heat transfer.Due to the limitations of analyt-ical methods in handling complex geometries and boundary conditions,we employ the FTCS scheme.The problem is formulated with Dirichlet boundary conditions and a sinusoidal initial condition for which an exact analytical so-lution is known.We derive the FTCS discretization using Taylor series-based approximations and perform a detailed von Neumann stability analysis to es-tablish the Courant-Friedrichs-Lewy(CFL)condition.The scheme’s perfor-mance is evaluated through numerical simulations on a uniform grid,with results compared against the exact solution.Simulation results show that the FTCS scheme achievesL2 and max-norm errors on the order of 10-11 and 10-10,respectively,under stable conditions.Graphical comparisons further demon-strate excellent agreement between numerical and analytical solutions.Over-all,the FTCS method proves to be a robust and reliable tool for solving heat conduction problems,provided the stability criterion is satisfied.展开更多
Compressed air energy storage(CAES)caverns transformed from horseshoe-shaped roadways in abandoned coal mines still face unclear mechanisms of force transfer,especially in the presence of initial damage in the surroun...Compressed air energy storage(CAES)caverns transformed from horseshoe-shaped roadways in abandoned coal mines still face unclear mechanisms of force transfer,especially in the presence of initial damage in the surrounding rock.The shape and size of the initial damage area as well as their effect on cavern stability remain unclear.Due to the complex geometry and multiphysical couplings,traditional numerical algorithms encounter problems of nonconvergence and low accuracy.These challenges can be addressed through numerical simulations with robust convergence and high accuracy.In this study,the damage area shapes of a CAES cavern are first computed using the concept of damage levels.Then,an iteration algorithm is improved using the generalization a method through the error control and one-way coupling loop for fully coupling equations.Finally,the stability of the CAES cavern with different damage zone shapes is numerically simulated in the thermodynamic process.It is found that this improved algorithm can greatly enhance numerical convergence and accuracy.The nonuniformity of the elastic modulus has a significant impact on the mechanical responses of the CAES cavern.The cavern shape with different damage zones has significant impacts on cavern stability.The initial damage area can delay the responses of temperature and stress.It induces variations of temperature in the range of approximately 1.2 m and variations of stress in the range of 1.5 m from the damage area.展开更多
The method of nonlinear finite element reliability analysis (FERA) of slope stability using the technique of slip surface stress analysis (SSA) is studied. The limit state function that can consider the direction of s...The method of nonlinear finite element reliability analysis (FERA) of slope stability using the technique of slip surface stress analysis (SSA) is studied. The limit state function that can consider the direction of slip surface is given, and the formula-tions of FERA based on incremental tangent stiffness method and modified Aitken accelerating algorithm are developed. The limited step length iteration method (LSLIM) is adopted to calculate the reliability index. The nonlinear FERA code using the SSA technique is developed and the main flow chart is illustrated. Numerical examples are used to demonstrate the efficiency and robustness of this method. It is found that the accelerating convergence algorithm proposed in this study proves to be very efficient for it can reduce the iteration number greatly, and LSLIM is also efficient for it can assure the convergence of the iteration of the reliability index.展开更多
We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with rea...We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When 0 ≥ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h 〉 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.展开更多
Analytical techniques and Liapunov method were used for the estimation of the attraction domain of memory patterns and local exponential stability of neural networks. The results were used to design efficient continuo...Analytical techniques and Liapunov method were used for the estimation of the attraction domain of memory patterns and local exponential stability of neural networks. The results were used to design efficient continuous feedback associative memory neural networks. The neural network synthesis procedure ensured the gain of large exponential convergence rate without reduction of the attraction domain.展开更多
We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. I...We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system. Furthermore, we obtain the long-time stability and convergence of the difference scheme and the upper semicontinuity d（Ah,τ, .A） → O. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.展开更多
In this paper,we study the convergence of a second-order finite volume approximation of the scalar conservation law.This scheme is based on the generalized Riemann problem(GRP)solver.We first investigate the stability...In this paper,we study the convergence of a second-order finite volume approximation of the scalar conservation law.This scheme is based on the generalized Riemann problem(GRP)solver.We first investigate the stability of the GRP scheme and find that it might be entropy-unstable when the shock wave is generated.By adding an artificial viscosity,we propose a new stabilized GRP scheme.Under the assumption that numerical solutions are uniformly bounded,we prove the consistency and convergence of this new GRP method.展开更多
The basic features of the colluvial deposit slope in Zuoyituo such as geological conditions, dimensions, slip surfaces and groundwater conditions are described concisely in this paper. The formation mechanism of the s...The basic features of the colluvial deposit slope in Zuoyituo such as geological conditions, dimensions, slip surfaces and groundwater conditions are described concisely in this paper. The formation mechanism of the slope is discussed. It is considered that the formation of the colluvial deposit slope in Zuoyituo has undergone accumulation, slip, load, deformation and failure. The effects of rainfall on slope stability are categorized systematically based on existing methodology, and ways to determine the effects quantitatively are presented. The remained slip force method is improved by the addition of quantitative relations to the existing formulae and programs. The parameters of the colluvial deposit slope are determined through experimentation and the method of back-analysis. The safety factors of the slope are calculated with the improved remained slip force method and the Sarma method. The results show that rainfall and water level in the Yangtze River have a significant effect on the stability of the colluvial deposit slope in Zuoyituo. The hazards caused by the instability of the slope are assessed, and prevention methods are put forward.展开更多
The convergence of the maximum entropy method of nonsmooth semi-infinite programmings is proved, and the stability and the strong stability of the method are discussed.
文摘In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
基金supported by the National Natural Science Foundation of China(Grant No.42377191,42072300)“The 14th Five Year Plan”Hubei Provincial advantaged characteristic disciplines(groups)project of Wuhan University of Science and Technology(Grant No.2023A0303).
文摘The stability of the tunnel portal slope is crucial for ensuring safe tunnel construction.Thus,a sound stability evaluation is of significance.Given the unique geological characteristics of tunnel portal slopes,it is necessary to establish a specific evaluation indicator system that differs from those used for ordinary slopes.Based on the unascertained measure method,uncertainties in the indicator are addressed by introducing the left and right half cloud asymmetric cloud model to optimize the linear membership function.The subjectivity of confidence criterion level identification is also improved by using the Euclidean distance method.Thus,a stability evaluation model for the tunnel portal slope is established based on the improved unascertained measure method.Finally,using the collected tunnel portal slope data,the results of four evaluation methods are compared with the safety factor levels.The evaluation methods include the traditional unascertained measure method,the method improved by using the left and right half cloud asymmetric cloud model,the method improved by using the Euclidean distance method,and the method improved by using both the left and right half cloud asymmetric cloud model and the Euclidean distance method.The results show that the accuracy rates of these four methods are 50%,55%,85%,and 90%,respectively.Among them,the joint improvement method has the slightest deviation,with only one level,while the other three methods had deviations of two levels.This result verifies the stability and effectiveness of the joint improvement method,providing a reference for tunnel portal slope stability evaluation.
文摘Alternating direction implicit (A.D.I.) schemes have been proved valuable in the approximation of the solutions of parabolic partial differential equations in multi-dimensional space. Consider equations in the form partial derivative u/partial derivative t - partial derivative/partial derivative x(a(x,y,t) partial derivative u/partial derivative x) - partial derivative/partial derivative y(b(x,y,t) partial derivative u partial derivative y) = f Two A.D.I. schemes, Peaceman-Rachford scheme and Douglas scheme will be studied. In the literature, stability and convergence have been analysed with Fourier Method, which cannot be extended beyond the model problem with constant coefficients. Additionally, L-2 energy method has been introduced to analyse the case of non-constant coefficients, however, the conclusions are too weak and incomplete because of the so-called 'equivalence between L-2 norm and H-1 semi-norm'. In this paper, we try to improve these conclusions by H-1 energy estimating method. The principal results are that both of the two A.D.I. schemes are absolutely stable and converge to the exact solution with error estimations O(Delta t(2) + h(2)) in discrete H-1 norm. This implies essential improvement of existing conclusions.
文摘The study of artificial slope stability has been a key item of geological engineering projects. Though more evaluation methods are available,result of stability evaluation simulation does not explain the actual problem owing to the diversified geological engineering factors and complexity. The author made a detailed study based on surveys of large amount of geological engineering research on Donggang Power Plant slope project,discussed the comprehensive factors influencing the project,and gave analytical calculation and evaluation to the improved response surface of the slope project. The study result shows that the slope is stable,which can provide scientific basis for designing the slope.
基金Supported by National Natural Science Foundation of China(10571036)the Key Discipline Development Program of Beijing Municipal Commission(XK100080537)
文摘This paper deals with the mean-square exponential input-to-state stability(exp-ISS)of Euler-Maruyama(EM)method applied to stochastic control systems(SCSs).The aim is to find out the conditions of the exact and EM method solutions to an SCS having the property of mean-square exp-ISS without involving control Lyapunov functions.Second moment boundedness and an appropriate form of strong convergence are achieved under global Lipschitz coeffcients and mean-square continuous random inputs.Under the strong convergent condition,it is shown that the mean-square exp-ISS of an SCS holds if and only if that of the EM method is preserved for suffciently small step size.
基金National Natural Science Foundation of China!No.69974018 Postdoctoral Science Foundation of China.
文摘Presents information on a study which dealt with the error behavior and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation as applied to the nonlinear delay differential equations. Methods and the basic lemmas; Analysis of convergence and stability.
文摘In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of thecharacteristics of a control dynamics system on its measured procedure will simplify thedecision method of movement stability problems.
基金supported by the Natural Science Foundation of China(Grant Nos.12271367,11771060)by the Science and Technology Innovation Plan of Shanghai,China(Grant No.20JC1414200)sponsored by the Natural Science Foundation of Shanghai,China(Grant No.20ZR1441200).
文摘Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach space.To break through the order barrier p≤1 of unconditionally contractive linear multistep methods for dissipative systems,strongly dissipative systems are introduced.By employing the error growth function of the methods,new contractivity and convergence results of stepsize-dependent linear multistep methods on infinite integration intervals are provided for strictly dissipative systems(ω<0)and strongly dissipative systems.Some applications of the main results to several linear multistep methods,including the trapezoidal rule,are supplied.The theoretical results are also illustrated by a set of numerical experiments.
基金supported by the Natural Science Foundation of Heilongjiang Province(Grant No.LH2022A020).
文摘In this paper,we investigate the theoretical and numerical analysis of the stochastic Volterra integro-differential equations(SVIDEs)driven by L´evy noise.The existence,uniqueness,boundedness and mean square exponential stability of the analytic solutions for SVIDEs driven by L´evy noise are considered.The split-step theta method of SVIDEs driven by L´evy noise is proposed.The boundedness of the numerical solution and strong convergence are proved.Moreover,its mean square exponential stability is obtained.Some numerical examples are given to support the theoretical results.
基金Wei Liu would like to thank Shanghai Rising-Star Program(Grant No.22QA1406900)Science and Technology Innovation Plan of Shanghai(Grant No.20JC1414200)the National Natural Science Foundation of China(Grant Nos.11871343,11971316 and 12271368)for their financial support.
文摘In this paper,numerical methods for the time-changed stochastic differential equations of the form dY(t)=a(Y(t))dt+b(Y(t))dE(t)+s(Y(t))dB(E(t))are investigated,where all the coefficients a(·),b(·)and s(·)are allowed to contain some super-linearly growing terms.An explicit method is proposed by using the idea of truncating terms that grow too fast.Strong convergence in the finite time of the proposed method is proved and the convergence rate is obtained.The proposed method is also proved to be able to reproduce the asymptotic stability of the underlying equation in the almost sure sense.Simulations are provided to demonstrate the theoretical results.
基金National Natural Science Foundation of China(Grant No.11971412)Key Project of Education Department of Hunan Province(Grant No.20A484)Project of Hunan National Center for Applied Mathematics(Grant No.2020ZYT003).
文摘A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further confirmed by some numerical experiments.Especially, the numerical method and its theories can be applied to specialcases, such as delay differential-algebraic equations and integral differential-algebraicequations.
文摘This paper presents a comprehensive numerical study of the two-dimensional time-dependent heat conduction equation using the Forward Time Centered Space(FTCS)finite difference scheme.The heat equation is a fundamental parabolic partial differential equation,models the diffusion of thermal energy in a medium and is applicable in areas such as thermal insulation design,mi-crochip cooling,and biological heat transfer.Due to the limitations of analyt-ical methods in handling complex geometries and boundary conditions,we employ the FTCS scheme.The problem is formulated with Dirichlet boundary conditions and a sinusoidal initial condition for which an exact analytical so-lution is known.We derive the FTCS discretization using Taylor series-based approximations and perform a detailed von Neumann stability analysis to es-tablish the Courant-Friedrichs-Lewy(CFL)condition.The scheme’s perfor-mance is evaluated through numerical simulations on a uniform grid,with results compared against the exact solution.Simulation results show that the FTCS scheme achievesL2 and max-norm errors on the order of 10-11 and 10-10,respectively,under stable conditions.Graphical comparisons further demon-strate excellent agreement between numerical and analytical solutions.Over-all,the FTCS method proves to be a robust and reliable tool for solving heat conduction problems,provided the stability criterion is satisfied.
基金National Key Research and Development Program of China,Grant/Award Number:2022YFE0129100National Natural Science Foundation of China,Grant/Award Number:51674246+1 种基金Graduate Innovation Program of China University of Mining and Technology,Grant/Award Number:2023WLJCRCZL046Postgraduate Research&Practice Innovation Program of Jiangsu Province,Grant/Award Number:KYCX23_2660。
文摘Compressed air energy storage(CAES)caverns transformed from horseshoe-shaped roadways in abandoned coal mines still face unclear mechanisms of force transfer,especially in the presence of initial damage in the surrounding rock.The shape and size of the initial damage area as well as their effect on cavern stability remain unclear.Due to the complex geometry and multiphysical couplings,traditional numerical algorithms encounter problems of nonconvergence and low accuracy.These challenges can be addressed through numerical simulations with robust convergence and high accuracy.In this study,the damage area shapes of a CAES cavern are first computed using the concept of damage levels.Then,an iteration algorithm is improved using the generalization a method through the error control and one-way coupling loop for fully coupling equations.Finally,the stability of the CAES cavern with different damage zone shapes is numerically simulated in the thermodynamic process.It is found that this improved algorithm can greatly enhance numerical convergence and accuracy.The nonuniformity of the elastic modulus has a significant impact on the mechanical responses of the CAES cavern.The cavern shape with different damage zones has significant impacts on cavern stability.The initial damage area can delay the responses of temperature and stress.It induces variations of temperature in the range of approximately 1.2 m and variations of stress in the range of 1.5 m from the damage area.
基金supported by the National Natural Science Foundation of China (No. 50748033)the Specific Foundation for PhD of Hefei University of Technology (No. 2007GDBJ044), China
文摘The method of nonlinear finite element reliability analysis (FERA) of slope stability using the technique of slip surface stress analysis (SSA) is studied. The limit state function that can consider the direction of slip surface is given, and the formula-tions of FERA based on incremental tangent stiffness method and modified Aitken accelerating algorithm are developed. The limited step length iteration method (LSLIM) is adopted to calculate the reliability index. The nonlinear FERA code using the SSA technique is developed and the main flow chart is illustrated. Numerical examples are used to demonstrate the efficiency and robustness of this method. It is found that the accelerating convergence algorithm proposed in this study proves to be very efficient for it can reduce the iteration number greatly, and LSLIM is also efficient for it can assure the convergence of the iteration of the reliability index.
基金supported by National Natural Science Foundation of China (Grant Nos. 91130003 and 11371157)the Scientific Research Innovation Team of the University “Aviation Industry Economy” (Grant No. 2016TD02)
文摘We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When 0 ≥ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h 〉 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.
文摘Analytical techniques and Liapunov method were used for the estimation of the attraction domain of memory patterns and local exponential stability of neural networks. The results were used to design efficient continuous feedback associative memory neural networks. The neural network synthesis procedure ensured the gain of large exponential convergence rate without reduction of the attraction domain.
基金The NSF (10871055) of Chinathe Fundamental Research Funds (HEUCFL20111102)for the Central Universities
文摘We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system. Furthermore, we obtain the long-time stability and convergence of the difference scheme and the upper semicontinuity d（Ah,τ, .A） → O. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.
基金funded by the Gutenberg Research College and by Chinesisch-Deutschen Zentrum fiur Wissenschaftsforderung(中德科学中心)Sino-German Project No.GZ1465M.L.is grateful to the Mainz Institute of Multiscale Modelling and SPP 2410 Hyperbolic Balance Laws in Fluid Mechanics:Complexity,Scales,Randomness(CoScaRa)for supporting her research.
文摘In this paper,we study the convergence of a second-order finite volume approximation of the scalar conservation law.This scheme is based on the generalized Riemann problem(GRP)solver.We first investigate the stability of the GRP scheme and find that it might be entropy-unstable when the shock wave is generated.By adding an artificial viscosity,we propose a new stabilized GRP scheme.Under the assumption that numerical solutions are uniformly bounded,we prove the consistency and convergence of this new GRP method.
文摘The basic features of the colluvial deposit slope in Zuoyituo such as geological conditions, dimensions, slip surfaces and groundwater conditions are described concisely in this paper. The formation mechanism of the slope is discussed. It is considered that the formation of the colluvial deposit slope in Zuoyituo has undergone accumulation, slip, load, deformation and failure. The effects of rainfall on slope stability are categorized systematically based on existing methodology, and ways to determine the effects quantitatively are presented. The remained slip force method is improved by the addition of quantitative relations to the existing formulae and programs. The parameters of the colluvial deposit slope are determined through experimentation and the method of back-analysis. The safety factors of the slope are calculated with the improved remained slip force method and the Sarma method. The results show that rainfall and water level in the Yangtze River have a significant effect on the stability of the colluvial deposit slope in Zuoyituo. The hazards caused by the instability of the slope are assessed, and prevention methods are put forward.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 19871049 and 19731001).
文摘The convergence of the maximum entropy method of nonsmooth semi-infinite programmings is proved, and the stability and the strong stability of the method are discussed.
