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1.
讨论分数阶微分方程和Adomian分解方法的应用.首先,回顾Adomian多项式的几种新的快速算法,包括单变量和多变量Adomian多项式.然后,讨论Rach-Adomian-Meyers修正分解方法、多级分解法和收敛加速概念,包括对角Pade近似和迭代Shanks变换.最后,研究Adomian分解法、修正分解法和收敛加速技术在分数阶微分方程求解中的应用.方法给出了容易计算、容易验证和迅速收敛的解析近似解序列.  相似文献   

2.
给出了一种新的改进Adomian分解方法,新方法能有效地解决传统Adomian分解方法及其改进方法的不足.将新改进方法应用于第二类Volterra积分方程、积分-微分方程求解,并与传统Adomian分解方法及其改进方法作比较分析,结果表明提出的新改进方法能返回方程精确解析解.  相似文献   

3.
四阶R-K方法中一类新算法的分析   总被引:1,自引:0,他引:1  
何满喜 《大学数学》2004,20(1):72-76
对常微分方程初值问题数值计算中的四阶R-K方法首次具体给出了一般格式中的参数所满足的方程,并提出了新的计算格式,这些新算法对某些初值问题其整体截断误差有明显的减少.这对常微分方程初值问题在社会、经济、生态等领域中的广泛应用将提供有益的新算法.  相似文献   

4.
在Hessian矩阵正定的前提下,建立一种最优曲线的微分方程模型.针对此微分方程模型,提出一种求解二次函数模型信赖域子问题的分段切线算法,并分析和证明分段切线路径的合理性.数值结果表明新算法是有效且可行的.  相似文献   

5.
在一阶广义Hukuhara导数的基础上定义了模糊值函数的二阶广义Hukuhara导数,利用该导数研究了二阶模糊微分方程的模糊初值问题,将二阶模糊微分方程转化成4个等价的常微分方程组,给出了模糊初值问题近似解析解的Adomian解法,文中给出了具体算例.  相似文献   

6.
联合Duffing方程和Van der Pol方程的非线性分数阶微分方程   总被引:1,自引:0,他引:1  
本文研究了Adomian分解方法在非线性分数阶微分方程求解中的应用. 利用Riemann-Liouville分数阶导数和Adomian分解方法, 将Duffing方程和Van der Pol方程联合在一个分数阶方程中,并获得了此方程的解析近似解.  相似文献   

7.
给出了一类具有多项式系数的二阶线性微分方程有多项式型特解和通解的充要条件,并在Maple下实现了这类微分方程具有多项式型特解和通解自动判定和求解的算法.  相似文献   

8.
谷伟  许文涛 《经济数学》2012,29(4):20-25
期权定价问题可以转化为对倒向随机微分方程的求解,进而转化为对相应抛物型偏微分方程的求解.为了求解与倒向随机微分方程相应的二阶拟线性抛物型微分方程初值问题,引入一类新的随机算法-分层方法取代传统的确定性数值算法.这种数值方法理论上是通过弱显式欧拉法,离散其相应随机系统解的概率表示而得到.该随机算法的收敛性在文中得到证明,其稳定性是自然的.并构造了易于数值实现的基于插值的算法,实证研究说明这种算法能很好地提供期权定价模型的数值模拟.  相似文献   

9.
给出了一个确定含参数偏微分方程(组)的完全对称分类微分特征列集算法,该算法能够直接、系统地确定偏微分方程(组)的完全对称分类.用给出的算法获得了含任意函数类参数的线性和非线性波动方程完全势对称分类.这也是微分形式特征列集算法(微分形式吴方法)在微分方程领域中的新应用.  相似文献   

10.
首先,我们给出了引入伴随方程(组)扩充原方程(组)的策略使给定偏微分方程(组)的扩充方程组具有对应泛瓯即,成为Lagrange系统的方法,以此为基础提出了作为偏微分方程(组)传统守恒律和对称概念的一种推广-偏微分方程(组)扩充守恒律和扩充对称的概念;其次,以得到的Lagrange系统为基础给定了确定原方程(组)扩充守恒律和扩充对称的方法,从而达到扩充给定偏微分方程(组)的首恒律和对称的目的;第三,提出了适用于一般形式微分方程(组)的计算固有守恒律的方法;第四,实现以上算法过程中,我们先把计算(扩充)守恒律和对称问题均归结为求解超定线性齐次偏微分方程组(确定方程组)的问题.然后,对此关键问题我们提出了用微分形式吴方法处理的有效算法;最后,作为方法的应用我们计算确定了非线性电报方程组在内的五个发展方程(组)的新守恒律和对称,同时也说明了方法的有效性.  相似文献   

11.
In this paper, a new improved Adomian decomposition method is proposed, which introduces a convergence-control parameter into the standard Adomian decomposition method and establishes a new iterative formula. The examples prove that the presented method is reliable, efficient, easy to implement from a computational viewpoint and can be employed to derive successfully analytical approximate solutions of fractional differential equations.  相似文献   

12.
A number of nonlinear phenomena in many branches of the applied sciences and engineering are described in terms of delay differential equations, which arise when the evolution of a system depends both on its present and past time. In this work we apply the Adomian decomposition method (ADM) to obtain solutions of several delay differential equations subject to history functions and then investigate several numerical examples via our subroutines in MAPLE that demonstrate the efficiency of our new approach. In our approach history functions are continuous across the initial value and its derivatives must be equal to the initial conditions (see Section 3) so that our results are more efficient and accurate than previous works.  相似文献   

13.
In this article, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when applied to partial differential equations of fractional order.  相似文献   

14.
In this work, we implement the natural decomposition method (NDM) to solve nonlinear partial differential equations. We apply the NDM to obtain exact solutions for three applications of nonlinear partial differential equations. The new method is a combination of the natural transform method and the Adomian decomposition method. We prove some of the properties that are related to the natural transform method. The results are compared with existing solutions obtained by other methods, and one can conclude that the NDM is easy to use and efficient. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

15.
Based on Adomian decomposition method, a new algorithm for solving boundary value problem (BVP) of nonlinear partial differential equations on the rectangular area is proposed. The solutions obtained by the method precisely satisfy all boundary conditions, except the small pieces near the four corners of the rectangular area. A theorem on the boundary error is given. Hence, the Adomian decomposition method is more efficiently applied to BVPs for partial differential equations. Segmented and weighted analytical solutions with a high accuracy for the BVP of nonlinear groundwater equations on a rectangular area are obtained by the present algorithm. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

16.
In this research paper, we examine a novel method called the Natural Decomposition Method (NDM). We use the NDM to obtain exact solutions for three different types of nonlinear ordinary differential equations (NLODEs). The NDM is based on the Natural transform method (NTM) and the Adomian decomposition method (ADM). By using the new method, we successfully handle some class of nonlinear ordinary differential equations in a simple and elegant way. The proposed method gives exact solutions in the form of a rapid convergence series. Hence, the Natural Decomposition Method (NDM) is an excellent mathematical tool for solving linear and nonlinear differential equation. One can conclude that the NDM is efficient and easy to use.  相似文献   

17.
In this article, we illustrate how the Adomian polynomials can be utilized with different types of iterative series solution methods for nonlinear equations. Two methods are considered here: the differential transform method that transforms a problem into a recurrence algebraic equation and the homotopy analysis method as a generalization of the methods that use inverse integral operator. The advantage of the proposed techniques is that equations with any analytic nonlinearity can be solved with less computational work due to the properties and available algorithms of the Adomian polynomials. Numerical examples of initial and boundary value problems for differential and integro-differential equations with different types of nonlinearities show good results.  相似文献   

18.
An orthogonal system of rational functions is derived from the mapped Laguerre polynomials, which is used for numerical solution of singular differential equations. A model problem is considered. A multiple-step algorithm is developed to implement this method. Numerical results show the efficiency of this new approach.  相似文献   

19.
In this article, we implement a relatively new numerical technique, Adomian’s decomposition method for solving the linear Helmholtz partial differential equations. The method in applied mathematics can be an effective procedure to obtain for the analytic and approximate solutions. A new approach to a linear or nonlinear problems is particularly valuable as a tool for Scientists and Applied Mathematicians, because it provides immediate and visible symbolic terms of analytic solution as well as its numerical approximate solution to both linear and nonlinear problems without linearization [Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, 1994; J. Math. Anal. Appl. 35 (1988) 501]. It does also not require discretization and consequently massive computation. In this scheme the solution is performed in the form of a convergent power series with easily computable components. This paper will present a numerical comparison with the Adomian decomposition and a conventional finite-difference method. The numerical results demonstrate that the new method is quite accurate and readily implemented.  相似文献   

20.
In this article, we proposed an auxiliary parameter method using Adomian polynomials and Laplace transformation for nonlinear differential equations. This method is called the Auxiliary Laplace Parameter Method (ALPM). The nonlinear terms can be easily handled by the use of Adomian polynomials. Comparison of the present solution is made with the existing solutions and excellent agreement is noted. The fact that the proposed technique solves nonlinear problems without any discretization or restrictive assumptions can be considered as a clear advantage of this algorithm over the numerical methods.  相似文献   

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