时滞Lokta-Volterra生态模型的同伦分析解法

研究了时滞Lolta-Volterra生态模型.利用同伦分析方法,得到了该模型解的近似展开式,并对近似解与数值解进行了比较.比较结果表明,近似解具有较高的精度,该方法用于生态模型研究可行.     

非线性Duffing扰动振子共振机制的研究

研究了一类广义Duffing扰动共振机制.利用泛函分析同伦映射方法,构造了求得问题渐近解的迭代关系式.首先求出了Duffing模型的初始近似函数;其次利用迭代关系依次求出了模型的各次渐近解;然后通过举例,说明了用泛函同伦映射方法得到的广义Duffing扰动振子随机共振机制的近似解简单而有效.讨论了得到的渐近解的意义.     

流行性传染病动力学模型的近似解

研究了一类流行性传染病.描述了传播动力学的生态模型.利用同伦映射理论和方法,得到了相应模型的近似解.     

一类非线性双曲型发展方程的孤子解

研究了一类非线性发展方程.首先在无扰动情形下,利用待定函数和泛函同伦映射方法得到了非扰动发展方程的孤子精确解和扰动方程的任意次近似行波孤子解.接着引入一个同伦映射,并选取初始近似函数,再用同伦映射理论,依次求出非线性双曲型发展扰动方程孤子解的各次近似解析解.再利用摄动理论举例说明了用该方法得到的近似解析解的有效性和各次近似解的近似度.最后,简述了用同伦映射方法得到的近似解的意义,指出了用上述方法得到的各次近似解具有便于求解、精度高等优点.     

带常利率的离散时间风险模型的破产概率

本文研究带常利率的离散时间的风险模型,得出了保险公司最终破产概率的一个近似解.给出了估计破产概率的上下界的表达式,并得到近似解的误差估计值.最后将结果应用到当保费服从指数分布这一特殊情况.     

带可分配工期的总误工问题的应急管理

本文考虑了单机排序中带可分配工期的总误工问题的应急管理问题.针对不同情况建立不同的模型,利用交换和动态规划的方法,得到了每个模型的最优解或近似解.     

一类非线性方程边值问题的匹配渐近解

利用匹配方法考虑了一类非线性方程边值问题的角层解.首先,由退化问题来决定问题的角层的位置.然后,构造零次近似的外部解和零次近似的内层解,并且对零次近似的外部解和零次近似的内层解进行匹配,由此便得到解的零次近似的形式合成展开式.继而构造一次近似的外部解和一次内层解,并且对一次近似的外部解和一次近似的内层解进行匹配,由此便得到解的一次近似的形式合成展开式.最后利用微分不等式理论证明了得到的一次近似的合成展开式是一致有效的渐近展开式.     

非线性强迫扰动Klein-Gordon方程的孤波渐近解法

研究了一类非线性强迫扰动Klein-Gordon方程.首先利用双曲正切待定系数法求得了典型的方程孤波解.然后利用泛函变分迭代原理得到了强迫扰动Klein-Gordon方程的一个近似解,并论述了解的一致有效性.所得到的近似解是一个解析式,它还可对近似解进行解析运算,而使用简单的模拟方法所得到的近似解是达不到这种效果的.     

一类大气尘埃等离子体扩散模型研究

研究了一类大气非线性尘埃等离子体扩散方程初值问题.首先在无扰动情形下,利用Fourier变换方法得到了尘埃等离子体扩散方程初值问题的精确解,接着引入一个同伦映射,并选取初始近似函数,再用同伦映射理论,依次求出了非线性尘埃等离子体扰动初值问题的各次近似解析解.并引用不动点理论,指出了近似解析解的有效性和各次近似解的近似度,通过举例, 用模拟曲线和表格作了近似对照.最后,简述了用同伦映射方法得到的近似解的物理意义.简叙了用上述方法得到的各次近似解具有便于求解、精度高等优点.     

泊松方程及平面弹性问题有限元方法中求高阶导数的提取法

在许多有限元计算中经常在求得近似解后还要求得到近似的解的导数.如在弹性计算中,如何从计算得到的位移近似解较好地计算应力早已被研究多年.如果计算中包含直接对近似解求导数,必然会丧失部分精度,得不到满意的结果.特别,若近似解为分片常数函数,则根本无法从直接求导数得到应力的近似值.Babuska和 Miller提出了所谓“提取法”,即利用推导出来的提取公式来求解的导数的近似值,以得到与近似解本身同     

A new method to build confidence regions for solutions of stochastic variational inequalities

Stochastic variational inequalities model a large class of equilibrium problems subject to data uncertainty. The true solution to such a problem is usually estimated by a solution to its sample average approximation (SAA) problem. This article proposed a new method to build asymptotically exact confidence regions for the true solution that are computable from the SAA solution.     

Order-optimal methods for the approximation of a piecewise-continuous solution to a certain inverse problem

The authors propose an order-optimal method for the approximation of a piecewise-continuous solution to a certain inverse problem and obtain exact by order bounds for the error of this approximation in the uniform metrics on segments of continuity of the exact solution to the problem.     

Cubic spline for a class of singular two-point boundary value problems

In this paper we have presented a method based on cubic splines for solving a class of singular two-point boundary value problems. The original differential equation is modified at the singular point then the boundary value problem is treated by using cubic spline approximation. The tridiagonal system resulting from the spline approximation is efficiently solved by Thomas algorithm. Some model problems are solved, and the numerical results are compared with exact solution.     

An approximation for kanban controlled assembly systems

An approximation is proposed to evaluate the steady-state performance of kanban controlled two-stage assembly systems. The development of the approximation is as follows. The considered continuous-time Markov chain is aggregated keeping the model exact, and this aggregate model is approximated replacing some state-dependent transition rates with constant rates. The approximate aggregate model is, then, decomposed into submodels and a product-form steady-state distribution is obtained for each submodel. Finally, the submodels are combined in such a way that the size of the problem becomes independent of the number of kanbans. This leads to the computational advantage in solving the combined model using numerical matrix-geometric solution algorithms. Numerical comparisons of the combined model with simulation, exact model, approximate aggregate model and an approximation in the literature show that the proposed approximation performs well in terms of accuracy and computational burden.     

再生核空间中求解带有积分边界条件的半线性热传导方程

该文给出了一个新的方法来求解带有积分边界条件的半线性热传导方程.方程的精确解以级数的形式在再生核空间中给出.证明了精确解的n项逼近是收敛于精确解的.同时给出了一些算例说明了这个方法的有效性.     

Finding the one‐loop soliton solution of the short‐pulse equation by means of the homotopy analysis method

The homotopy analysis method is applied to the short‐pulse equation in order to find an analytic approximation to the known exact solitary upright‐loop solution. It is demonstrated that the approximate solution agrees well with the exact solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear solitary waves. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

A Feed-Forward Neural Network for Solving Stokes Problem

The current research attempts to offer a novel method for solving the Stokes problem based on the use of feed-forward neural networks. We transform the mixed Stokes problem into three independent Poisson problems which by solving them the solution of the Stokes problem is obtained. The results obtained by this method, has been compared with the existing numerical method and with the exact solution of the problem. It can be observed that the current new approximation has higher accuracy. The number of model parameters required is less than conventional methods. The proposed new method is illustrated by two examples.     

A numerical method to solve a class of linear integro‐differential equations with weakly singular kernel

In this paper, a collocation method based on the Bessel polynomials is introduced for the approximate solution of a class of linear integro‐differential equations with weakly singular kernel under the mixed conditions. The exact solution can be obtained if the exact solution is polynomial. In other cases, increasing number of nodes, a good approximation can be obtained with applicable errors. In addition, the method is presented with error and stability analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive symplectic conservative numerical methods for the Kepler problem

We suggest and substantiate a unified form of a family of adaptive conservative numerical methods for the Kepler problem. The family contains methods of the second, fourth, and sixth approximation order as well as an exact method. The methods preserve all the global properties of the exact solution of the problem. The variable time step is chosen automatically depending on the properties of the solution.     

Point approximation of a space-homogeneous transport equation

Summary We present an approximation method of a space-homogeneous transport equation which we prove is convergent. The method is very promising for numerical computation. Comparison of a numerical computation with an exact solution is given for the Master equation.