This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem...
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This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem(CLT)of the temporal average of the BEM method,which characterizes its asymptotics in *** the deviation order is smaller than the optimal strong order,we directly derive the CLT of the temporal average through that of original equations and the uniform strong order of the BEM *** the case that the deviation order equals to the optimal strong order,the CLT is established via the Poisson equation associated with the generator of original *** experiments are performed to illustrate the theoretical *** main contribution of this work is to generalize the existing CLT of the temporal average of numerical methods to that for SODEs with super-linearly growing drift coefficients.
This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpola...
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This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpolation, a class of adapted Runge-Kutta(ARK) methods are developed. Under the suitable conditions, it is proved that ARK methods are convergent of order min{p, μ+ν +1}, where p is the consistency order of ARK methods and μ, ν are two given parameters in Lagrange interpolation. Moreover, a global stability criterion is derived for ARK methods. With some numerical experiments, the computational accuracy and global stability of ARK methods are further testified.
We present a decoupled,linearly implicit numerical scheme with energy stability and mass conservation for solving the coupled Cahn-Hilliard *** time-discretization is done by leap-frog method with the scalar auxiliary...
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We present a decoupled,linearly implicit numerical scheme with energy stability and mass conservation for solving the coupled Cahn-Hilliard *** time-discretization is done by leap-frog method with the scalar auxiliary variable(SAV)*** only needs to solve three linear equations at each time step,where each unknown variable can be solved *** is shown that the semi-discrete scheme has second-order accuracy in the temporal *** convergence results are proved by a rigorous analysis of the boundedness of the numerical solution and the error estimates at different *** examples are presented to further confirm the validity of the methods.
This paper is concerned with the numerical solution of Volterra integro-differential equations with noncompact *** focus is on the problems with weakly singular *** handle the initial weak singularity of the solution,...
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This paper is concerned with the numerical solution of Volterra integro-differential equations with noncompact *** focus is on the problems with weakly singular *** handle the initial weak singularity of the solution,a fractional collocation method is applied.A rigorous hp-version error analysis of the numerical method under a weighted H1-norm is carried *** result shows that the method can achieve high order convergence for such *** experiments are also presented to confirm the effectiveness of the proposed method.
In this paper,we consider numerical solutions of the fractional diffusion equation with theαorder time fractional derivative defined in the Caputo-Hadamard sense.A high order time-stepping scheme is constructed,analy...
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In this paper,we consider numerical solutions of the fractional diffusion equation with theαorder time fractional derivative defined in the Caputo-Hadamard sense.A high order time-stepping scheme is constructed,analyzed,and numerically *** contribution of the paper is twofold:1)regularity of the solution to the underlying equation is investigated,2)a rigorous stability and convergence analysis for the proposed scheme is performed,which shows that the proposed scheme is 3+αorder *** numerical examples are provided to verify the theoretical statement.
New and evolving cyber attacks against smart grids are emerging. This necessitates that the network intrusion detection systems (IDSs) have online learning ability. However, most existing methods struggle to handle ne...
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In order to accurately receive early warning of the cascading failures caused by coordinated cyber-attacks(CFCC)in grid cyber-physical systems(GCPS),an adaptive early warning method of CFCC is ***,the evolutionary mec...
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In order to accurately receive early warning of the cascading failures caused by coordinated cyber-attacks(CFCC)in grid cyber-physical systems(GCPS),an adaptive early warning method of CFCC is ***,the evolutionary mechanism of CFCC is analyzed from the attackers'view,the CFCC mathematical model is established,and the transition processes of GCPS running states under the influence of CFCC staged failures are ***,the mathematical model of the adaptive early warning method is ***,the mathematical model of the adaptive early warning method is mapped as an adaptive control process with tolerating staged failures damage,and the solving process is presented to infer the CFCC and its next evolution trend.A decision-making idea for the optimal active defense scheme is proposed considering the costs and gains of various defense ***,to verify the effectiveness of the adaptive early warning method,the warning and defense processes of a typical CFCC are simulated in a GCPS experimental system based on CEPRI-36 BUS.
In this study of optimizing the dynamic characteristics of the manipulator, with the increase of motion redundancy, the complexity of solving the inverse motion problem increases significantly, making it extremely cha...
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Spectral differentiations are basic ingredients of spectral methods. In this work, we analyze the pointwise rate of convergence of spectral differentiations for functions containing singularities and show that the det...
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This paper enriches the topological horseshoe theory using finite subshift theory in symbolic dynamical systems, and develops an elementary framework addressing incomplete crossing and semi-horseshoes. Two illustrativ...
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