高阶非线性薛定谔方程的Adomian分解

利用Maple计算了Adomian多项式获得的序列解,由此,给出了高阶非线性薛定谔方程的Adomian分解法。结果说明,利用Adomian分解可以得到非线性问题的近似解。     

Neural network method for solving elastoplastic finite element problems

INTRODUCTION An Artificial Neural Network (ANN) is an in-formation-processing paradigm that is inspired by the way biological nervous systems, such as the brain, process information. It is composed of a large number of highly interconnected processing elements (neu-rons) working in unison to solve specific problems. In recent years, neural network has been widely applied in the field of engineering construction as a large dimensional nonlinear dynamic system, because of its support for …     

用非规则节点解偏微分方程的局部微分求积法

In the conventional differential quadrature (DQ) method the functional values along a mesh line are used toapproximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature (LDQ)method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximatedby a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in thenew approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directlyapproximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature isstill kept. Numerical examples are provided to validate the LDQ method.     

求高次方程整数解的递套方法

给出了n维长方体套及其测度的概念，使用递套方法，得到求高次方程整数解的新方法。     

求解常微分方程的函数逼近法

提出了一种利用函数逼近法求解常微分方程(ODE)初值问题的数值方法。在多项式空间中寻找函数,在某种距离意义下尽可能满足微分方程,从而获得微分方程的近似解。通过理论分析可知,求解常微分方程的欧拉法、梯形法是该方法的特例,数值试验进一步表明了该方法的有效性。     

二阶延迟微分方程Runge-Kutta方法的稳定性

研究二阶延迟微分方程Runge-Kutta方法的稳定性.首先,引入新变量,将二阶延迟微分方程化为一阶方程组.然后,应用Runge-Kuta 方法于一阶方程组,给出了Runge-Kutta稳定的充分条件,进而得到了二阶延迟微分方程Runge-Kutta方法稳定的充分条件.最后,通过数值试验验证所得结论的正确性.     

求解恰当方程的一个新方法

对恰当方程的结构进行了分析．把方程适当组合,提出了一种求解恰当方程的新方法,使得求解恰当方程更为快捷．新方法与传统的方法相比,节约了一半的工作量．     

The Embedding Method for Nonsmooth Equations

1IntroductionTherehavebeenmailystudiesonnonsllloothequatiollsl"'"]F(x)=0,FiD=R"-R",((l.l)butfewauthorsusedembedding1lletllodtosolve'theequations(1.l).In1990,S.M.RobinsonstudiedthenonsnlootllembeddingmethodforaclassofBdifferentiableequationsill[51.WhenFiss…     

符号计算与非线性偏微分方程精确行波解

In this paper, with the aid of the symbolic computation, a further extended tanh function method was presented. Based on the new general ansatz, many nonlinear partial differential equation（s）（NPDE（s）） can he solved. Especially, as applications, a compound KdV-mKdV equation and the Broer-Kaup equations are considered successfully, and many solutions including periodic solutions, triangle solutions, and rational solutions are obtained. The method can also be applied to other NPDEs.     

抛物型积分-微分方程的交替方向有限元方法

对一类抛物型积分一微分方程提出了一种全离散交替方向有限元格式，分析了该格式的收敛性，得到了最佳H^1模误差估计。     

一般FPK方程近似求解的局部Galerkin方法

１　Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｔｈｅｓｔｏｃｈａｓｔｉｃｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ（ＳＤＥ）ａｒｅｕｓｅｄｉｎｍａｎｙａｒｅａｓｏｆｓｃｉｅｎｃｅａｎｄｅｎｇｉｎｅｅｒｉｎｇ．ＴｈｅｍａｉｎｐｕｒｐｏｓｅｆｏｒｓｏｌｖｉｎｇｐｒｏｂｌｅｍｓｗｉｔｈＳＤＥｉｓｔｏｏｂｔａｉｎｔｈｅｐｒｏｂａｂｉｌｉｔｙｄｅｎｓｉｔｙｆｕｎｃｔｉｏｎ（ＰＤＦ）ｏｆｔｈｅｓｔａｔｅｖａｒｉａｂｌｅｓｇｏｖｅｒｎｅｄｂｙｔｈｅＳＤＥｂｅｃａｕｓｅｍａｎｙｏｔｈｅｒｓｔａｔｉｓｔｉｃａｌａｎａｌｙｓｉｓａ…     

解Lyapunov 矩阵方程的改进的梯度迭代算法

In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared with the GI algorithm, the improved algorithm reduces computational cost and storage. Finally, the algorithm is tested with GI several numerical examples.     

An inexact parameterized newton method for B-differentiable equations

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ１９９５,ＭａｒｔｉｎｅｚａｎｄＱｉ［６］ｐｒｏｐｏｓｅｄａｎｏｎｓｍｏｏｔｈｖｅｒｓｉｏｎｏｆｉｎｅｘａｃｔＮｅｗｔｏｎｍｅｔｈｏｄ：ｘｋ＋１＝ｘｋ＋ｄｋ‖Ｖｋｄｋ＋Ｆ（ｘｋ）‖≤αｋ‖Ｆ（ｘｋ）‖,αｋ＞０Ｖｋ∈Ｂ...     

傅里叶变换在求解微分方程中的应用

傅里叶变换在数学领域中有着广泛的应用,本文主要从三个方面来讨论傅里叶变换方法在求解偏微分方程中的具体运用;即:利用傅立叶变换将线性偏微分方程转换为代数方程、常微分方程然后求解;傅里叶变换在解常微分方程中的具体应用;特别是这类化归方法在某些重要常微分方程中的运用;通过分析,掌握这类方法在具体运用中的局限性,从而合理地选择方法来求解具体给定的常微分方程定解问题。     

解Sylvester方程组的全局似极小残差法

Abstract In this paper, a global quasi-minimal residual （QMR） method was presented for solving the Sylvester equations. Some properties were investigated with a new matrix product for the global QMR method. Numerical results with the global QMR and GMRES methods compared with the block GMRES method were given. The results show that the global QMR method is less time-consuming than the global GMRES （generalized minimal residual） and block GMRES methods in some cases.     

求解非线性约束优化问题的一个数值延拓算法

1　IntroductionThenonlinearconstrainedoptimizationproblemisaveryimportantmathematicalprogrammingprob lem .Ithasbeenstudiedextensively ,andmanyalgo rithmsforsolvingthis problemhasbeen pro posed[1,2 ] .Mostalgorithmsforsolvingthenonlinearcon strainedoptimization problemislocallyconvergent ,suchastheNewtonmethod ,theBFGSmethodandtheSQPmethod ,etc .Toovercomethisdrawback ,manyextendediterativemethodshavebeendevel oped .Forexample ,theNewtonmethodincorporatedwiththelinesearch[1] andhomotopymeth…     

弦截法在非线性方程组的推广

通过对求解非线性方程组的牛顿方法的研究,在介绍了求解非线性方程的弦截法和快速弦截法的基础上,给出了求解非线性方程组的弦截法。非线性方程组的弦截法实际上是弦截法从非线性方程的一个推广,该推广避免了牛顿方法在求解非线性方程组的过程中出现导数为0,或很小时带来的困难。还给出了弦截法求解非线性方程组的详细步骤,并结合具体算例验证了该方法的收敛性以及收敛速度。     

Implicit iterative method for III-posed equations with perturbed operators and data

In this paper, the author applied an implicit iterative method to solve linear ill-posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactory order of convergence rate was derived. Supported by the National Natural Science Foundation of China (19671050)     

定常Navier-Stokes方程加罚形式的两重网格算法

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＮｕｍｅｒｉｃａｌｌｙｓｏｌｖｉｎｇｔｈｅｉｎｃｏｍｐｒｅｓｓｉｂｌｅＮａｖｉｅｒ Ｓｔｏｋｅｓｅｑｕａｔｉｏｎｓｈａｓｔｗｏｄｉｆｆｉｃｕｌｔｉｅｓ :ｔｈｅｎｏｎｌｉｎｅａｒｆｏｒｍａｎｄｔｈｅｉｎｃｏｍｐｒｅｓｓｉｂｉｌｉｔｙｃｏｎｄｉｔｉｏｎ .Ｉｎｔｈｉｓｐａ ｐｅｒ ,ｗｅｃｏｎｓｉｄｅｒｔｈｅａｐｐｒｏｘｉｍａｔｉｏｎｂｙａ ｐｅｎａｌｔｙｍｅｔｈｏｄｆｏｒｔｈｅＮａｖｉｅｒ Ｓｔｏｋｅｓｅｑｕａｔｉｏｎｓｔｏｃｏｐｅｗｉｔｈｔｈｅｓｅｃｏｎｄｄｉｆｆｉｃｕｌｔ…     

利用指数函数法求Kudryashov-Sinelshchikov方程的精确行波解

Kudryashov-Sinelshchikov(K-S)方程具有重要的物理背景和研究意义,很多学者对其精确解进行了研究,在=-3和=-4时得到了各种形式的精确行波解.本文利用指数函数法对该方程的精确行波解进行了研究,获得了该方程在任意参数条件下具有一般形式的精确行波解,包括孤立波解和周期波解,将原有的结果进行了有效的推广.