利用变分迭代法解二阶常微分方程组边值问题

将变分迭代法用于求解二阶常微分方程组边值问题,给出方法在两个具体实例中的应用,验证了变分迭代法对求解线性、非线性二阶常微分方程组边值问题是一种非常简便有效的方法.     

变分迭代法在抛物型方程反问题中的应用

本文将改进的变分迭代法的应用范围加以推广,使其应用于多维抛物型方程反问题中。它通过Lagrange乘子进行简便计算求得未知参量的精确值,再应用于多维抛物型方程反问题可以快速得到收敛于反问题精确解的收敛序列,从而得到精确解。同时,通过与Adomian’s分裂法结果比较可知前者比分裂法好。     

利用变分迭代技术解时滞微分方程

应用变分迭代法这种较新的迭代技术解具有初值条件的时滞微分方程.通过这种方法,获得了它的数值解和精确解.通过一些实例充分地说明了这种方法是有效地和便捷的,所得的值与精确解相比较,进一步表明了这种方法的可靠性和精确性.而且这种方法还能被应用到其它领域.     

变分迭代法解时滞微分方程(英文)

变分迭代法被用于解时滞微分方程,通过这种方法我们得到了他们的准确解和数值解。一些例子说明了这种方法的有效性,结果显示这种方法对于解时滞微分方程是一种有力的直接的数学方法。     

任意变系数微分方程的精确解析法

工程中的许多问题归结为求解任意变系数微分方程的解.本文首次提出精确解析法,用以求解任意变系数微分方程在任意边界条件下的解.文中还给出精确解析法的一般计算格式,得到了一致收敛于精确解及其任意阶导数的解析表达式,并给出收敛性证明.文末给出四个算例,均得到较好的结果,证明了本文理论的正确性.     

大型线性方程组的变分迭代解法

本文提出了一种求解大型线性方程组的一种新方法——变分迭代解法．这种方法的基本思想是：先给方程一个近似的初值,然后引进若干个拉氏乘子校正其近似值,而拉氏乘子可用极值的概念最佳确定．这种方法收敛速度较快,如果只取ｎ个拉氏乘子（ｎ为方程个数）,则该方法即为Ｎｅｗｔｏｎ迭代法．     

求解变分不等式和互补问题的一种迭代法

最近,有限维的非线性变分不等式和互补问题的研究有了较快的发展,具体可见Harker和Pang的综述性文献。但是,在没有(强)单调性及可微性的条件下,却没有一个实用的算法。本文的主要兴趣是研究一种迭代算法—外梯度,在连续性和伪单调性条件下,证明了算法的全局收敛性(定理3.1)。     

求解HJB方程的拟变分不等式组的迭代法

本文对HJB方程的拟变分不等式组提出一种迭代算法,并给出此算法在一定的条件下的单调性定理和证明,数值试验表明此法有效的.     

光测弹性理论中的耦联变分原理和广义耦联变分原理

在本文中,应用拉格朗日乘子法和高阶拉格朗日乘子法[1],我们系统地导出了光测弹性理论中的耦联势能原理,耦联余能原理和具有二类和三类变量的广义耦联势能原理和广义相联余能原理。     

多比例延迟微分方程的散逸性

本文讨论多比例延迟微分方程的散逸性，给出了多比例延迟微分方程是散逸的充分条件，它可视为文献[8]中相应结果的推广。     

Modified Variational Iteration Method for Heat and Wave-Like Equations

In this paper, we apply the modified variational iteration method (MVIM) for solving the heat and wave-like equations. The proposed modification is made by introducing He’s polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that proposed technique solves nonlinear problems without using the Adomian’s polynomials can be considered as a clear advantage of this algorithm over the decomposition method.     

Application of Homotopy Perturbation Method and Variational Iteration Method to Nonlinear Oscillator Differential Equations

In this paper, homotopy perturbation method (HPM) and variational iteration method (VIM) are applied to solve nonlinear oscillator differential equations. Illustrative examples reveal that these methods are very effective and convenient for solving nonlinear differential equations. Moreover, the methods do not require linearization or small perturbation. Comparisons are also made between the exact solutions and the results of the homotopy perturbation method and variational iteration method in order to prove the precision of the results obtained from both methods mentioned.     

病态线性方程组新的Jacobi迭代解法

给出了解病态线性方程组的一种新的Jacobi迭代算法,并证明了算法的收敛性;通过具体算例说明了算法的实用性和有效性.     

非线性变延迟微分方程隐式Euler法的渐近稳定性

本讨论非线性变延迟微分方程隐式Euler法的渐近稳定性。我们证明，在方程真解渐近稳定的条件下，隐式Euler法也是渐近稳定的。     

随机延迟微分方程的Milstein方法的非线性均方稳定性

本文针对一般的非线性随机延迟微分方程,证明了当系统理论解满足均方稳定性条件时,则当方程的漂移和扩散项满足一定的条件时,Milstein方法也是均方稳定的.数学实验进一步验证了我们的结论.     

Variational iteration method for solving the space‐ and time‐fractional KdV equation

This paper presents numerical solutions for the space‐ and time‐fractional Korteweg–de Vries equation (KdV for short) using the variational iteration method. The space‐ and time‐fractional derivatives are described in the Caputo sense. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers in the functionals can be identified optimally via variational theory. The iteration method, which produces the solutions in terms of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and accurate when applied to space‐ and time‐fractional KdV equations. The method introduces a promising tool for solving many space–time fractional partial differential equations. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007     

Convergence Aspects of Step-Parallel Iteration of Runge-Kutta Methods for Delay Differential Equations

Implicit Runge-Kutta methods are known as highly accurate and stable methods for solving differential equations. However, the iteration technique used to solve implicit Runge-Kutta methods requires a lot of computational efforts. To lessen the computational effort, one can iterate simultaneously at a number of points along the t-axis. In this paper, we extend the PDIRK (Parallel Diagonal Iterated Runge-Kutta) methods to delay differential equations (DDEs). We give the region of convergence and analyze the speed of convergence in three parts for the P-stability region of the Runge-Kutta corrector. It is proved that PDIRK methods to DDEs are efficient, and the diagonal matrix D of the PDIRK methods for DDES can be selected in the same way as for ordinary differential equations (ODEs).