In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approxim...In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approximation and introduce a sequence of linear second-order SBVPs.We prove that the solution of the SBVP with regularized noise converges to the solution of the original SBVP with convergence order O(h)in the meansquare sense.To obtain a numerical solution,we apply the finite difference method to the stochastic BVP whose noise is piecewise constant approximation of the original noise.The approximate SBVP with regularized noise is shown to have better regularity than the original problem,which facilitates the convergence proof for the proposed scheme.Convergence analysis is presented based on the standard finite difference method for deterministic problems.More specifically,we prove that the finite difference solution converges at O(h)in the mean-square sense,when the second-order accurate three-point formulas to approximate the first and second derivatives are used.Finally,we present several numerical examples to validate the efficiency and accuracy of the proposed scheme.展开更多
This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p...This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p} under the Lipschitz condition and the linear growth condition, where p is the exponent of HSlder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter p the derived method can have a better stability property than more commonly used numerical methods. That is, for some p, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters p. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient.展开更多
Massive multiple-input multiple-output(MIMO) system is capable of substantially improving the spectral efficiency as well as the capacity of wireless networks relying on equipping a large number of antenna elements at...Massive multiple-input multiple-output(MIMO) system is capable of substantially improving the spectral efficiency as well as the capacity of wireless networks relying on equipping a large number of antenna elements at the base stations. However, the excessively high computational complexity of the signal detection in massive MIMO systems imposes a significant challenge for practical hardware implementations. In this paper, we propose a novel minimum mean square error(MMSE) signal detection using the accelerated overrelaxation(AOR) iterative method without complicated matrix inversion, which is capable of reducing the overall complexity of the classical MMSE algorithm by an order of magnitude. Simulation results show that the proposed AOR-based method can approach the conventional MMSE signal detection with significant complexity reduction.展开更多
Two new convection-dominated are derived under the approximate solutions least-squares mixed finite element procedures are formulated for solving Sobolev equations. Optimal H（div;Ω）×H1（Ω） norms error estima...Two new convection-dominated are derived under the approximate solutions least-squares mixed finite element procedures are formulated for solving Sobolev equations. Optimal H（div;Ω）×H1（Ω） norms error estimates standard mixed finite spaces. Moreover, these two schemes provide the with first-order and second-order accuracy in time increment, respectively.展开更多
Numerical algorithms for stiff stochastic differential equations are developed using lin-ear approximations of the fast diffusion processes,under the assumption of decoupling between fast and slow processes.Three nume...Numerical algorithms for stiff stochastic differential equations are developed using lin-ear approximations of the fast diffusion processes,under the assumption of decoupling between fast and slow processes.Three numerical schemes are proposed,all of which are based on the linearized formulation albeit with different degrees of approximation.The schemes are of comparable complexity to the classical explicit Euler-Maruyama scheme but can achieve better accuracy at larger time steps in stiff systems.Convergence analysis is conducted for one of the schemes,that shows it to have a strong convergence order of 1/2 and a weak convergence order of 1.Approximations arriving at the other two schemes are discussed.Numerical experiments are carried out to examine the convergence of the schemes proposed on model problems.展开更多
In this paper, we combine a split least-squares procedure with the method of characteristics to treat convection-dominated parabolic integro-differential equations. By selecting the least-squares functional properly, ...In this paper, we combine a split least-squares procedure with the method of characteristics to treat convection-dominated parabolic integro-differential equations. By selecting the least-squares functional properly, the procedure can be split into two independent sub-procedures, one of which is for the primitive unknown and the other is for the flux. Choosing projections carefully, we get optimal order H^1 （Ω） and L^2（Ω） norm error estimates for u and sub-optimal （L^2（Ω））^d norm error estimate for σ. Numerical results are presented to substantiate the validity of the theoretical results.展开更多
The purpose of this study was to clarify grid convergence property of three-dimensional measurement-integrated (3D-MI) simulation for a flow behind a square cylinder with Karman vortex street. Measurement-integrated (...The purpose of this study was to clarify grid convergence property of three-dimensional measurement-integrated (3D-MI) simulation for a flow behind a square cylinder with Karman vortex street. Measurement-integrated (MI) simulation is a kind of the observer in the dynamical system theory by using CFD scheme as a mathematical model of the system. In a former study, two-dimensional MI (2D-MI) simulation with a coarse grid system showed a fairly good result in comparison with a 2D ordinary (2D-O) simulation, but the results were degraded with grid refinement. In this study, 3D-MI simulation and three-dimensional ordinary (3D-O) simulation were performed with three grid systems of different grid resolutions, and their grid convergence properties were compared. As a result, all 3D-MI simulations reproduced the vortex shedding frequency identical to that of the experiment, and the flow fields obtained were very close, within 5% difference between the results, while the results of the 3D-O simulations showed variation of the solution under convergence. It is shown that the grid convergence property of 3D-MI simulation is monotonic and better than that of 3D-O simulation, whereas those of 2D-O and 2D-MI simulations for streamwise velocity fluctuation are divergent. The solution of 3D-MI simulation with a relatively coarse grid system properly reproduces the basic three-dimensional structure of the wake flow as well as the drag and lift coefficients.展开更多
The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied.An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desi...The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied.An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order.In general the proposed symplectic schemes are fully implicit,and they become computationally expensive for mean square orders greater than two.However,for stochastic Hamiltonian systems preserving Hamiltonian functions,the high-order symplectic methods have simpler forms than the explicit Taylor expansion schemes.A theoretical analysis of the convergence and numerical simulations are reported for several symplectic integrators.The numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.展开更多
We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation.The approximation is based on freezing the...We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation.The approximation is based on freezing the velocity on time subintervals resulting in a linear stochastic parabolic equation for vorticity.At each time step,the velocity is expressed via vorticity using a formula corresponding to the Biot-Savart-type law.We prove the first mean-square convergence order of the vorticity approximation.展开更多
This study deal with seven points finite difference method to find the approximation solutions in the area of mean square calculus solutions for linear random parabolic partial differential equations. Several numerica...This study deal with seven points finite difference method to find the approximation solutions in the area of mean square calculus solutions for linear random parabolic partial differential equations. Several numerical examples are presented to show the ability and efficiency of this method.展开更多
In the paper, a result of Walsh and Sharma on least square convergence of Lagrange interpolation polynomials based on the n-th roots of unity is extended to Lagrange interpolation on the sets obtained by projecting ve...In the paper, a result of Walsh and Sharma on least square convergence of Lagrange interpolation polynomials based on the n-th roots of unity is extended to Lagrange interpolation on the sets obtained by projecting vertically the zeros of (1-x)2=P (a,β) n(x),a>0,β>0,(1-x)P(a,β) n(x),a>0,β>-1,(1+x)P P(a,β) n(x),a>-1,β0 and P(a,β) n(x),a>-1,β>-1, respectively, onto the unit circle, where P(a,β) n(x),a>-1,β>-1, stands for the n-th Jacobi polynomial. Moreover, a result of Saff and Walsh is also extended.展开更多
Nature inspired optimization algorithms have made substantial step towards solving of various engineering and scientific real-life problems.Success achieved for those evolution-ary optimization techniques are due to s...Nature inspired optimization algorithms have made substantial step towards solving of various engineering and scientific real-life problems.Success achieved for those evolution-ary optimization techniques are due to simplicity and flexibility of algorithm structures.In this paper,optimal set of filter coefficients are searched by the evolutionary optimiza-tion technique called Opposition-based Differential Evolution(ODE)for solving infinite impulse response(IIR)system identification problem.Opposition-based numbering con-cept is embedded into the primary foundation of Differential Evolution(DE)technique metaphorically to enhance the convergence speed and the performance for finding the optimal solution.The population is generated with the evaluation of a solution and its opposite solution by fitness function for choosing potent solutions for each iteration cycle.With this competent population,faster convergence speed and better solution quality are achieved.Detailed and balanced search in multidimensional problem space is accomplished with judiciously chosen control parameters for mutation,crossover and selection adopted in the basic DE technique.When tested against standard benchmark examples,for same order and reduced order models,the simulation results establish the ODE as a competent candidate to others in terms of accuracy and convergence speed.展开更多
为了解决遗传算法的收敛速度和全局收敛性之间的矛盾,本文提出了一种改进的自适应遗传算法Adaptive GA Based on Square Error(SEAGA)。在原自适应遗传算法Adaptive GA(AGA)的基础上提出用适应度方差函数来监控种群的进化情况并据此自...为了解决遗传算法的收敛速度和全局收敛性之间的矛盾,本文提出了一种改进的自适应遗传算法Adaptive GA Based on Square Error(SEAGA)。在原自适应遗传算法Adaptive GA(AGA)的基础上提出用适应度方差函数来监控种群的进化情况并据此自动调整算法的交叉率和变异率的思想。通过用此算法对测试函数进行计算,并与SGA,AGA的结果进行比较,可以看出本算法在收敛速度和全局搜索性上优于其它同类算法。展开更多
An improved moving least square meshless method is developed for the numerical solution of the nonlinear improved Boussinesq equation. After the approximation of temporal derivatives, nonlinear systems of discrete alg...An improved moving least square meshless method is developed for the numerical solution of the nonlinear improved Boussinesq equation. After the approximation of temporal derivatives, nonlinear systems of discrete algebraic equations are established and are solved by an iterative algorithm. Convergence of the iterative algorithm is discussed. Shifted and scaled basis functions are incorporated into the method to guarantee convergence and stability of numerical results. Numerical examples are presented to demonstrate the high convergence rate and high computational accuracy of the method.展开更多
Econometric simultaneous equation models play an important role in making economic policies, analyzing economic structure and economic forecasting. This paper presents local linear estimators by TSLS with variable ban...Econometric simultaneous equation models play an important role in making economic policies, analyzing economic structure and economic forecasting. This paper presents local linear estimators by TSLS with variable bandwidth for every structural equation in semi-parametric simultaneous equation models in econometrics. The properties under large sample size were studied by using the asymptotic theory when all variables were random. The results show that the estimators of the parameters have consistency and asymptotic normality, and their convergence rates are equal to n^-1/2. And the estimator of the nonparametric function has the consistency and asymptotic normality in interior points and its rate of convergence is equal to the optimal convergence rate of the nonparametric function estimation.展开更多
The efficient management of ambulance routing for emergency requests is vital to save lives when a disaster occurs.Quantum-behaved Particle Swarm Optimization(QPSO)algorithm is a kind of metaheuristic algorithms appli...The efficient management of ambulance routing for emergency requests is vital to save lives when a disaster occurs.Quantum-behaved Particle Swarm Optimization(QPSO)algorithm is a kind of metaheuristic algorithms applied to deal with the problem of scheduling.This paper analyzed the motion pattern of particles in a square potential well,given the position equation of the particles by solving the Schrödinger equation and proposed the Binary Correlation QPSO Algorithm Based on Square Potential Well(BC-QSPSO).In this novel algorithm,the intrinsic cognitive link between particles’experience information and group sharing information was created by using normal Copula function.After that,the control parameters chosen strategy gives through experiments.Finally,the simulation results of the test functions show that the improved algorithms outperform the original QPSO algorithm and due to the error gradient information will not be over utilized in square potential well,the particles are easy to jump out of the local optimum,the BC-QSPSO is more suitable to solve the functions with correlative variables.展开更多
基金partially supported by the NASA Nebraska Space Grant Program and UCRCA at the University of Nebraska at Omaha.
文摘In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approximation and introduce a sequence of linear second-order SBVPs.We prove that the solution of the SBVP with regularized noise converges to the solution of the original SBVP with convergence order O(h)in the meansquare sense.To obtain a numerical solution,we apply the finite difference method to the stochastic BVP whose noise is piecewise constant approximation of the original noise.The approximate SBVP with regularized noise is shown to have better regularity than the original problem,which facilitates the convergence proof for the proposed scheme.Convergence analysis is presented based on the standard finite difference method for deterministic problems.More specifically,we prove that the finite difference solution converges at O(h)in the mean-square sense,when the second-order accurate three-point formulas to approximate the first and second derivatives are used.Finally,we present several numerical examples to validate the efficiency and accuracy of the proposed scheme.
基金This work is supported by National Natural Science Foundation of China （Nos. 11401594, 11171125, 91130003） and the New Teachers＇ Specialized Research Fund for the Doctoral Program from Ministry of Education of China （No. 20120162120096）.
文摘This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p} under the Lipschitz condition and the linear growth condition, where p is the exponent of HSlder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter p the derived method can have a better stability property than more commonly used numerical methods. That is, for some p, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters p. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient.
基金supported by the key project of the National Natural Science Foundation of China (No. 61431001)Huawei Innovation Research Program, the 5G research program of China Mobile Research Institute (Grant No. [2015] 0615)+2 种基金the open research fund of National Mobile Communications Research Laboratory Southeast University (No.2017D02)Key Laboratory of Cognitive Radio and Information Processing, Ministry of Education (Guilin University of Electronic Technology)the Foundation of Beijing Engineering and Technology Center for Convergence Networks and Ubiquitous Services, and Keysight
文摘Massive multiple-input multiple-output(MIMO) system is capable of substantially improving the spectral efficiency as well as the capacity of wireless networks relying on equipping a large number of antenna elements at the base stations. However, the excessively high computational complexity of the signal detection in massive MIMO systems imposes a significant challenge for practical hardware implementations. In this paper, we propose a novel minimum mean square error(MMSE) signal detection using the accelerated overrelaxation(AOR) iterative method without complicated matrix inversion, which is capable of reducing the overall complexity of the classical MMSE algorithm by an order of magnitude. Simulation results show that the proposed AOR-based method can approach the conventional MMSE signal detection with significant complexity reduction.
基金Supported by by the National Science Foundation for Young Scholars of China(11101431)the Fundamental Research Funds for the Central Universities (12CX04082A,10CX04041A)Shandong Province Natural Science Foundation of China(ZR2010AL020)
文摘Two new convection-dominated are derived under the approximate solutions least-squares mixed finite element procedures are formulated for solving Sobolev equations. Optimal H（div;Ω）×H1（Ω） norms error estimates standard mixed finite spaces. Moreover, these two schemes provide the with first-order and second-order accuracy in time increment, respectively.
文摘Numerical algorithms for stiff stochastic differential equations are developed using lin-ear approximations of the fast diffusion processes,under the assumption of decoupling between fast and slow processes.Three numerical schemes are proposed,all of which are based on the linearized formulation albeit with different degrees of approximation.The schemes are of comparable complexity to the classical explicit Euler-Maruyama scheme but can achieve better accuracy at larger time steps in stiff systems.Convergence analysis is conducted for one of the schemes,that shows it to have a strong convergence order of 1/2 and a weak convergence order of 1.Approximations arriving at the other two schemes are discussed.Numerical experiments are carried out to examine the convergence of the schemes proposed on model problems.
基金The NSF(11101431 and 11201485)of Chinathe NSF(ZR2010AL020)of Shandong Province
文摘In this paper, we combine a split least-squares procedure with the method of characteristics to treat convection-dominated parabolic integro-differential equations. By selecting the least-squares functional properly, the procedure can be split into two independent sub-procedures, one of which is for the primitive unknown and the other is for the flux. Choosing projections carefully, we get optimal order H^1 （Ω） and L^2（Ω） norm error estimates for u and sub-optimal （L^2（Ω））^d norm error estimate for σ. Numerical results are presented to substantiate the validity of the theoretical results.
文摘The purpose of this study was to clarify grid convergence property of three-dimensional measurement-integrated (3D-MI) simulation for a flow behind a square cylinder with Karman vortex street. Measurement-integrated (MI) simulation is a kind of the observer in the dynamical system theory by using CFD scheme as a mathematical model of the system. In a former study, two-dimensional MI (2D-MI) simulation with a coarse grid system showed a fairly good result in comparison with a 2D ordinary (2D-O) simulation, but the results were degraded with grid refinement. In this study, 3D-MI simulation and three-dimensional ordinary (3D-O) simulation were performed with three grid systems of different grid resolutions, and their grid convergence properties were compared. As a result, all 3D-MI simulations reproduced the vortex shedding frequency identical to that of the experiment, and the flow fields obtained were very close, within 5% difference between the results, while the results of the 3D-O simulations showed variation of the solution under convergence. It is shown that the grid convergence property of 3D-MI simulation is monotonic and better than that of 3D-O simulation, whereas those of 2D-O and 2D-MI simulations for streamwise velocity fluctuation are divergent. The solution of 3D-MI simulation with a relatively coarse grid system properly reproduces the basic three-dimensional structure of the wake flow as well as the drag and lift coefficients.
文摘The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied.An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order.In general the proposed symplectic schemes are fully implicit,and they become computationally expensive for mean square orders greater than two.However,for stochastic Hamiltonian systems preserving Hamiltonian functions,the high-order symplectic methods have simpler forms than the explicit Taylor expansion schemes.A theoretical analysis of the convergence and numerical simulations are reported for several symplectic integrators.The numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.
文摘We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation.The approximation is based on freezing the velocity on time subintervals resulting in a linear stochastic parabolic equation for vorticity.At each time step,the velocity is expressed via vorticity using a formula corresponding to the Biot-Savart-type law.We prove the first mean-square convergence order of the vorticity approximation.
文摘This study deal with seven points finite difference method to find the approximation solutions in the area of mean square calculus solutions for linear random parabolic partial differential equations. Several numerical examples are presented to show the ability and efficiency of this method.
基金NSFC under grant1 0 0 71 0 3 9and by Education Committee of Jiangsu Province under grant0 0 KJB1 1 0 0 0 5 .
文摘In the paper, a result of Walsh and Sharma on least square convergence of Lagrange interpolation polynomials based on the n-th roots of unity is extended to Lagrange interpolation on the sets obtained by projecting vertically the zeros of (1-x)2=P (a,β) n(x),a>0,β>0,(1-x)P(a,β) n(x),a>0,β>-1,(1+x)P P(a,β) n(x),a>-1,β0 and P(a,β) n(x),a>-1,β>-1, respectively, onto the unit circle, where P(a,β) n(x),a>-1,β>-1, stands for the n-th Jacobi polynomial. Moreover, a result of Saff and Walsh is also extended.
文摘Nature inspired optimization algorithms have made substantial step towards solving of various engineering and scientific real-life problems.Success achieved for those evolution-ary optimization techniques are due to simplicity and flexibility of algorithm structures.In this paper,optimal set of filter coefficients are searched by the evolutionary optimiza-tion technique called Opposition-based Differential Evolution(ODE)for solving infinite impulse response(IIR)system identification problem.Opposition-based numbering con-cept is embedded into the primary foundation of Differential Evolution(DE)technique metaphorically to enhance the convergence speed and the performance for finding the optimal solution.The population is generated with the evaluation of a solution and its opposite solution by fitness function for choosing potent solutions for each iteration cycle.With this competent population,faster convergence speed and better solution quality are achieved.Detailed and balanced search in multidimensional problem space is accomplished with judiciously chosen control parameters for mutation,crossover and selection adopted in the basic DE technique.When tested against standard benchmark examples,for same order and reduced order models,the simulation results establish the ODE as a competent candidate to others in terms of accuracy and convergence speed.
文摘为了解决遗传算法的收敛速度和全局收敛性之间的矛盾,本文提出了一种改进的自适应遗传算法Adaptive GA Based on Square Error(SEAGA)。在原自适应遗传算法Adaptive GA(AGA)的基础上提出用适应度方差函数来监控种群的进化情况并据此自动调整算法的交叉率和变异率的思想。通过用此算法对测试函数进行计算,并与SGA,AGA的结果进行比较,可以看出本算法在收敛速度和全局搜索性上优于其它同类算法。
基金Project supported by the National Natural Science Foundation of China(Grant No.11971085)the Fund from the Chongqing Municipal Education Commission,China(Grant Nos.KJZD-M201800501 and CXQT19018)the Chongqing Research Program of Basic Research and Frontier Technology,China(Grant No.cstc2018jcyjAX0266)。
文摘An improved moving least square meshless method is developed for the numerical solution of the nonlinear improved Boussinesq equation. After the approximation of temporal derivatives, nonlinear systems of discrete algebraic equations are established and are solved by an iterative algorithm. Convergence of the iterative algorithm is discussed. Shifted and scaled basis functions are incorporated into the method to guarantee convergence and stability of numerical results. Numerical examples are presented to demonstrate the high convergence rate and high computational accuracy of the method.
基金This project is supported by National Natural Science Foundation of China （70371025）
文摘Econometric simultaneous equation models play an important role in making economic policies, analyzing economic structure and economic forecasting. This paper presents local linear estimators by TSLS with variable bandwidth for every structural equation in semi-parametric simultaneous equation models in econometrics. The properties under large sample size were studied by using the asymptotic theory when all variables were random. The results show that the estimators of the parameters have consistency and asymptotic normality, and their convergence rates are equal to n^-1/2. And the estimator of the nonparametric function has the consistency and asymptotic normality in interior points and its rate of convergence is equal to the optimal convergence rate of the nonparametric function estimation.
基金This research was funded by National Key Research and Development Program of China(Grant No.2018YFC1507005)China Postdoctoral Science Foundation(Grant No.2018M643448)+1 种基金Sichuan Science and Technology Program(Grant No.2019YFG0110)Fundamental Research Funds for the Central Universities,Southwest Minzu University(Grant No.2019NQN22).
文摘The efficient management of ambulance routing for emergency requests is vital to save lives when a disaster occurs.Quantum-behaved Particle Swarm Optimization(QPSO)algorithm is a kind of metaheuristic algorithms applied to deal with the problem of scheduling.This paper analyzed the motion pattern of particles in a square potential well,given the position equation of the particles by solving the Schrödinger equation and proposed the Binary Correlation QPSO Algorithm Based on Square Potential Well(BC-QSPSO).In this novel algorithm,the intrinsic cognitive link between particles’experience information and group sharing information was created by using normal Copula function.After that,the control parameters chosen strategy gives through experiments.Finally,the simulation results of the test functions show that the improved algorithms outperform the original QPSO algorithm and due to the error gradient information will not be over utilized in square potential well,the particles are easy to jump out of the local optimum,the BC-QSPSO is more suitable to solve the functions with correlative variables.
