CONVERGENCE OF MODIFIED TRUNCATED EULER-MARUYAMA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH HOLDER DIFFUSION COEFFICIENTS

Convergence of modified truncated Euler-Maruyama(MTEM)method for stochastic differential equations(SDEs)with(1/2+α)-Holder continuous diffusion coefficients are investigated in this paper.We prove that the MTEM method for SDE converges to the exact solution in L9 sense under given conditions.Two examples are provided to support our conclusions.

Periodic folded waves for a (2+1)-dimensional modified dispersive water wave equation

A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.

NONLINEAR STABILITY OF TRUNCATED SHALLOW CONICAL SANDWICH SHELL WITH VARIABLE THICKNESS

The theory of nonlinear stability for a truncated shallow conical shell with variable thickness under the action of uniform pressure was presented. The fundamental equations and boundary conditions were derived by means of calculus of variations. An analytic solution for the critical buckling pressure of the shell with a hyperbolically varying thickness is obtained by use of modified iteration method. The results of numerical calculations are presented in diagrams, which show the influence of geometrical and physical parameters on the buckling behavior.

Convergence Rates for the Truncated Euler-Maruyama Method for Nonlinear Stochastic Differential Equations

In this paper,our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients.When the diffusion coefficient is polynomially growing or linearly growing,the strong convergence rate of arbitrarily close to one half is established at a single time T or over a time interval[0.T],respectively.In both situations,the common one-sided Lipschitz and polynomial growth conditions for the drift coefficients are not required.Two examples are provided to illustrate the theory.

THE CONVERGENCE OF TRUNCATED EULER-MARUYAMA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH PIECEWISE CONTINUOUS ARGUMENTS UNDER GENERALIZED ONE-SIDED LIPSCHITZ CONDITION

In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.

Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments

In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition.The order of convergence is obtained.Moreover,we show that the truncated EM method can preserve the exponential mean square stability of SDEPCAs.Numerical examples are provided to support our conclusions.

Strong convergence rate of truncated Euler-Maruyama method for stochastic differential delay equations with Poisson jumps

We study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are investigated under the generalized Khasminskii-type condition.

Principle of MSD floating-point division based on Newton-Raphson method on ternary optical computer

The division operation is not frequent relatively in traditional applications, but it is increasingly indispensable and important in many modern applications. In this paper, the implementation of modified signed-digit （MSD） floating-point division using Newton-Raphson method on the system of ternary optical computer （TOC） is studied. Since the addition of MSD floating-point is carry-free and the digit width of the system of TOC is large, it is easy to deal with the enough wide data and transform the division operation into multiplication and addition operations. And using data scan and truncation the problem of digits expansion is effectively solved in the range of error limit. The division gets the good results and the efficiency is high. The instance of MSD floating-point division shows that the method is feasible.

CONVERGENCE RATE OF THE TRUNCATED EULER-MARUYAMA METHOD FOR NEUTRAL STOCHA STIC DIFFERENTIAL DELAY EQUATIONS WITH MARKOVIAN SWITCHING

The key aim of this paper is to show the strong convergence of the truncated Euler-Maruyama method for neutral stochastic differential delay equations(NSDDEs)with Markovian switching(MS)without the linear growth condition.We present the truncated Euler-Maruyama method of NSDDEs-MS and consider its moment boundedness under the local Lipschitz condition plus Khasminskii-type condition.We also study its strong convergence rates at time T and over a finite interval[0,T].Some numerical examples are given to illustrate the theoretical results.

瞬变电磁波场转换算法的改进

地球物理电磁场数据与虚拟地震波场数据之间存在数学上的等效转换关系,通过这种等效转换,可有效提高地球物理电磁法对地下目标体分界面的辨识度.但是这种转换在数学上属于不适定问题,可采用奇异值分解法处理.由于大奇异值控制计算矩阵的主要信息,小的奇异值控制计算矩阵的次要信息,传统的截断奇异值分解法只保留大奇异值,而忽略小的奇异值,导致数值解不够精确.本文提出一种新的修正方案——改进截断奇异值法,采用岭估计方法计算由小的奇异值引起的虚拟波场.模型计算结果表明:改进截断奇异值法比传统的奇异值分解法得到的波场转换结果更好,对某煤矿采空区探测数据进行了处理,成功分辨出采空区分界面.

变厚度夹层截顶扁锥壳的非线性稳定性分析

对具有变厚度夹层截顶扁锥壳的非线性稳定问题进行了研究· 利用变分原理导出表层为等厚度而夹心为变厚度的夹层截顶扁锥壳的非线性稳定问题的控制方程和边界条件 ,采用修正迭代法求得了具有双曲型变厚度夹层截顶扁锥壳的非线性稳定性问题的解析解 ,得到了内边缘与一刚性中心固结而外边缘为可移夹紧固支的变厚度夹层截顶扁锥壳临界屈曲载荷的解析表达式 ,讨论了几何参数和物理参数对壳体屈曲行为的影响·

基于混沌理论的SCCPM联合迭代解调译码算法

针对DVB-RCS2下行链路物理层中定义的串行级联连续相位调制信号迭代检测中存在的系统复杂度高、低信噪比条件下收敛性较差的问题,从匹配滤波器组和迭代译码两方面对系统进行改进,提出了一种基于混沌理论的联合迭代解调译码算法。该算法利用修正高斯小波函数的快速收敛特性来控制混沌迭代过程的动态区,并且结合延迟反馈控制法,有效抑制了迭代译码中暂态混沌对系统性能的影响,改善了系统在低信噪比条件下的收敛性,同时减少了迭代译码的次数。为了进一步解决计算迭代译码中的码字先验信息需要大量匹配滤波器的问题,通过计算协方差矩阵的条件数可得有效匹配滤波器具有很强相关性,提出的算法使用截断小特征值法来减弱这种相关性,从而对匹配滤波器组进行简化,在实际应用中仅使用4个匹配滤波器即可满足要求。仿真结果表明,提出的算法与传统算法相比,可以有效地降低系统复杂度,同时具有良好的迭代收敛性,并且适用于所有类型的CPM调制方案。

双层网格开顶扁球壳的非线性稳定性分析

根据基于等效夹层壳思想的双层网格圆底扁球壳在极坐标下的平衡方程、相容方程,采用修正迭代法,对外边缘滑动固定、内边缘悬空和外边缘夹紧固定、内边缘悬空两种边界条件下,双层网格开顶圆底扁球壳的非线性稳定性进行了分析,得出了非线性载荷-位移关系及临界荷载的解析表达式,并讨论和分析了网壳几何参数对临界屈曲载荷的影响。

梯形修正公式及其余项“中间点”的渐近性

给出了一种带端点导数的梯形修正公式,并给出了该公式的截断误差。分析了相应的复化求积公式的收敛阶,其收敛阶比复化梯形法提高了2阶;并通过对梯形修正公式余项的研究。讨论了该求积公式余项"中间点"的渐近性,使求积公式的代数精度得到进一步提高。

修正的截断展开法与(3+1)维KP方程新的精确解

在截断展开法和辅助方程方法的基础上,首次提出了修正的截断展开法,并利用该法求出了（3＋1）维KP方程许多新的精确解析解,其中包括三角函数类解,有理函数类解和双曲函数类解（含钟型孤子解）等.这些新解丰富了KP方程解析解的形式,也验证了修正的截断展开法在求解高维非线性发展方程中的重要作用.

Finite symmetry transformation group and localized structures of the (2+1)-dimensional coupled Burgers equation

In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.

The Traveling Wave Solutions for Some Nonlinear PDEs in Mathematical Physics

In the present article, we construct the exact traveling wave solutions of some nonlinear PDEs in the mathematical physics via (1 + 1) dimensional Kaup Kupershmit equation, the (1 + 1) dimensional seventh order KdV equation and (1 + 1) dimensional Kersten-Krasil Shchik equations by using the modified truncated expansion method. New exact solutions of these equations are found.

复合载荷下开顶扁球壳的非线性稳定问题

用修正迭代法讨论了开顶扁球壳在均布及中心集中载荷联合作用下的非线性稳定问题,得到了临界荷载的二次近似解。

中立型变时滞随机微分方程数值解的强收敛性

讨论中立型变时滞随机微分方程改进的修正截断Euler-Maruyama(EM)方法的q阶矩强收敛性,并得到收敛速度。结果表明此方法适用于高度非线性的漂移项和扩散项,且相较于隐式的修正截断EM方法计算量更小,适用范围更广。

求解基于路径的Logit型随机用户均衡模型的新算法

为了更高效地求解Logit型随机用户均衡模型,提出了一种改进的截断牛顿算法,该算法具有超线性的收敛速度。首先运用变量消去法,将Logit型随机用户均衡模型转化为一个无约束的最优化问题,再运用截断牛顿算法求解该最优化问题。在Sioux Falls网络上,对梯度投影法与改进的截断牛顿法进行了对比。计算结果表明:多数情况下,改进的截断牛顿法的计算效率高于梯度投影算法;在拥挤条件下,该算法的优势尤为明显。