求解随机微分方程split-step欧拉方法的收敛性

给出随机微分方程的split-step欧拉格式的算法,并证明了当方程的偏移系数和扩散系数均满足线性增长条件和李普希兹条件的情况下,此方法用以求解随机微分方程的收敛性,并且求出强收敛的阶是1/2.同时证明了split-step近似解的均方收敛理论.

一种特殊的Θ-method求解比例尺方程的收敛性分析(英文)

介绍了用偏序的概念去研究用一种特殊的Θ-method求解比例尺方程的数值解和解析解的收敛性,然后证明了使用该种特殊的Θ-method求解该比例尺方程的数值解和解析解的收敛性.对这类研究的目前状况做一个简短的研究.

带时滞随机泛函微分方程的Split-step算法

针对一类带有泊松跳的时变时滞随机泛函微分方程,基于Euler-Maruyama算法,给出了Split-step算法。在带跳时滞随机泛函微分方程的系数满足全局Lipschitz条件、线性增长条件和初值函数具有Hlder连续性的条件下,证明了文中的Split-step算法在均方意义下以0.5阶矩收敛。最后通过几个实例进行了数值模拟,验证了算法的有效性。

Adaptive split-step Fourier method for simulating ultrashort laser pulse propagation in photonic crystal fibres

In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.

General Modified Split-Step Balanced Methods for Stiff Stochastic Differential Equations

A class of general modified split-step balanced methods proposed in the paper can be applied to solve stiff stochastic differential systems with m-dimensional multiplicative noise. Compared to some other already reported split-step balanced methods, the drift increment function of the methods can be taken from any chosen ane-step ordinary differential equations （ODEs） solver. The schemes is proved to be strong convergent with order one. For the mean-square stability analysis, the investigation is confined to two cases. Some numerical experiments are reported to testify the performance and the effectiveness of the methods.

THE STABILITY OF θ-METHODS FOR PANTOGRAPH DELAY DIFFERENTIAL EQUATIONS

This paper deals with the numerical solution of initial value problems for pantograph differential equations with variable delays. We investigate the stability of one leg θ-methods in the numerical solution of these problems. Sufficient conditions for the asymptotic stability of θ-methods are given by Fourier analysis and Ergodic theory.

集成ISM与G1的建筑工人安全能力影响因素研究

为探究影响建筑工人安全能力的因素,提出一种集成解释结构模型(ISM)与序相关法(G1-Method)的因素分析法。首先,基于壳层模型(SHELL)与因子分析法,归纳与提取影响因素;其次,通过ISM构建工人安全能力影响因素多级递阶结构模型;最后,结合改进的G1-Method,计算因素间关联度及对安全能力的影响重要度。结果表明:所构建的安全能力影响因素结构模型包括安全认知能力、安全行为能力2个维度,以及16个影响因素。其中,安全观念、操作技能、环境适应是建筑工人安全能力形成的浅层因素,而安全教培、安全管理是安全能力形成的深层因素。同时,安全观念、安全教培、环境适应是安全认知能力的主要影响因素;操作技能、安全教培、安全管理是安全行为能力的主要影响因素。

Detection of Pulsation and Additional Components in Eclipsing Binary RS Sct

The eclipsing binary star RS Sct is a semi-detached system of theβLyrae type.This system was photometered for six nights in 2019 August,and 2020 June and August.The light and radial velocity curves were simultaneously analyzed to obtain the absolute physical and orbital parameters of the system,and the system geometry was determined.In this system,the primary component has filled its inner Roche lobe and the secondary component is close to filling it.Moreover,the change in the orbital period of this system was investigated.The presence of the third or fourth components and the mass transfer between the two components affect the orbital period of the system.In addition,the pulsation of the primary component was detected.Also,several frequencies with high signal-to-noise ratios were identified.According to the position of the primary component in the H-R diagram and the value of the obtained frequencies,this component is likely a delta-Scuti pulsator.

CONVERGENCE AND STABILITY OF THE SPLIT-STEP THETA METHOD FOR A CLASS OF STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS DRIVEN BY LEVY NOISE

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.

MODIFIED SPLIT-STEP THETA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION

For solving the stochastic differential equations driven by fractional Brownian motion,we present the modified split-step theta method by combining truncated Euler-Maruyama method with split-step theta method.For the problem under a locally Lipschitz condition and a linear growth condition,we analyze the strong convergence and the exponential stability of the proposed method.Moreover,for the stochastic delay differential equations with locally Lipschitz drift condition and globally Lipschitz diffusion condition,we give the order of convergence.Finally,numerical experiments are done to confirm the theoretical conclusions.

一类具有分布式记忆项的跳-扩散方程的分步随机θ方法

针对一类具有分布式记忆项与泊松跳的随机微分方程,构造了该方程的分步随机数值解,在局部Lipschitz条件下证明了分步随机θ数值解的均方收敛性以及收敛阶达到1/2.最后,证明了方程解的指数稳定性,并在此基础上,进一步证明了所构造的数值解的均方稳定性.

中立型随机延迟微分方程的分步θ-方法

研究非线性中立型随机延迟微分方程的分步θ-方法。在全局Lipschitz条件和线性增长条件下,证明分步θ-方法的均方收敛阶为1/2,给出中立型随机延迟微分方程分步θ-方法均方稳定的条件。数值算例说明,参数θ和步长h对分步θ-方法均方稳定性有影响。

蒸发波导中的电磁场分布研究

基于不稳定层结、中性层结、稳定层结的修正折射率剖面,利用抛物型方程的Fourier split-step算法得到了不同大气层结条件下中的空间场分布。以中性层结条件为例,基于电波传输损耗分析了蒸发波导中的雷达探测性能。

新型无条件稳定SSCN-FDTD算法

提出了一种新型的基于split-step方案和Crank-Nicolson方案的时域有限差分法(finite-difference time-domain method FDTD),并且证明了此种算法的无条件稳定性。所提出的算法采用新的矩阵分解形式,沿着x、y、z三个方向进行分解,将三维问题转化为一维问题,与alternating direction implicit(ADI)-FDTD算法、split-step(SS)-FDTD(1,2)算法和SS-FDTD(2,2)算法相比,减少了计算复杂度,提高了计算效率;同时所提出的算法具有二阶时间精度和二阶空间精度。新型算法的推导程序比基于指数因子分解的无条件FDTD算法更简单。将新型算法用于计算谐振腔结构,在计算相对误差一致的情况下,计算时间比ADI-FDTD算法节省约31%,比SS-FDTD(1,2)算法节省约13.5%。

金融领域的随机建模与基于软件R的Monte Carlo模拟(4):随机微分方程模型

主要研究线性随机微分方程模型,为此定义It随机微积分,建立It公式.鉴于研究的重点是利用R软件进行数值模拟,所以详细讨论了过去10多年来随机微分方程数值解的研究.

Intensity distribution function and statistical properties of fast radio bursts

Fast Radio Bursts （FRBs） are intense radio flashes from the sky that are characterized by mil- lisecond durations and Jansky-level flux densities. We carried out a statistical analysis on FRBs that have been discovered. Their mean dispersion measure, after subtracting the contribution from the interstellar medium of our Galaxy, is found to be ~ 660 pc cm-3, supporting their being from a cosmological origin. Their energy released in the radio band spans about two orders of magnitude, with a mean value of ~ 10-39 erg. More interestingly, although the study of FRBs is still in a very early phase, the published collection of FRBs enables us to derive a useful intensity distribution function. For the 16 non-repeating FRBs detected by the Parkes telescope and the Green Bank Telescope, the intensity distribution can be described as dN/dFobs = （4.1± 1.3） × 103 F-obs1.1±0.2 sky-1 d-l, where Fobs is the observed radio obs fluence in units of Jy ms. Here the power-law index is significantly flatter than the expected value of 2.5 for standard candles distributed homogeneously in a flat Euclidean space. Based on this intensity distribution function, the Five-hundred-meter Aperture Spherical radio Telescope （FAST） is predicted to be able to detect about five FRBs for every 1000 h of observation time.

The θ－Methods in Numerical Solution of Systems of Differential Equations with Two Delay Terms

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.

Wavelet Cleaning of Solar Dynamic Radio Spectrograms

By applying the state-of-the-art mathematical apparatus, the wavelet transformation, we explore the possibility of a dynamic cleaning of raw data ob- tained with the Chinese solar radio spectrographs over a wide wavelength range (from 0.7 to 7.6 GHz). We consider the problem of eliminating the interference caused by combination rates of data sampling (10-20 ins), and the low-frequency interference (4-30 s) caused by the receiving equipment changing its characteristics with time. It is shown that the best choice to reconstruct a signal suffering from amplitude, frequency and phase instabilities, is by means of wavelet transformation at both high and low frequencies. We analysed observational data which contained interferences of nonsolar origin such as instrumental effects and other man-made signals. A subsequent comparison of the reference data obtained with the acousto- optical receiver of the Siberian Solar Radio Telescope (SSRT) with the 'cleaned' spectra confirms the correctness of this approach.

Evolution of dark solitons in the presence of Raman gain and self-steepening effect

Based on the equation satisfied by optical pulse that is a slowly varying function, the higher-order nonlinear Schr o¨dinger equation(NLSE) including Raman gain and self-steepening effect is deduced in detail, and a new Raman gain function is defined. By using the split-step Fourier method, the influence of the combined effect between Raman gain and self-steepening on the propagation characteristic of dark solitons is simulated in the isotropic fiber. The results show that gray solitons can be symmetrically formed by high order dark soliton, however self-steepening effect will inhibit the formation mechanism through the phenomenon that gray solitons are produced only in the trailing edge of the central black soliton. Meanwhile, the Raman gain changes the propagation characteristic of optical soliton and inhibits the self-steepening effect, resulting in the broadening of pulse width and the decreasing of pulse offset.

Numerically investigating the peculiar periphery of a supernova remnant in the medium with a density gradient:the case of RCW 103

The young shell-type supernova remnant RCW 103 has peculiar properties in the X-ray morphology obtained with Chandra.The southeastern shell is brighter in the X-rays,and the curved border of the shell in this region is flatter than the other part.We investigate the formation of the peculiar periphery of the supernova remnant RCW 103 using 3D hydrodynamical simulation.Assuming that the supernova ejecta has been evolved in the medium with a density gradient,the detected shape of the periphery can be generally reproduced.For RCW 103,with the ejecta mass of 3.0 M,the density of the background material of 2.0 cm^(-3),and a gradient of 3.3-4.0 cm^(-3)pc^(-1),the X-ray periphery can be generally reproduced.The simulation turned out that the asymmetry of the SNR RCW 103 is mainly due to the inhomogeneous medium with a density gradient.