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1.
吕学琴  崔明根 《计算数学》2009,31(2):111-117
在再生核空间中给出一类二阶非线性偏微分方程的一个新的求解方法,近似解un(x)是通过在再生核空间中截断精确解u(x)而得到的,最后,通过一个数值算例来说明该方法是有效的.  相似文献   

2.
定义了再生核空间,在再生核空间中给出了一类带初、边值条件的非线性偏微分方程的数值解法,并给出了算法实例.  相似文献   

3.
吴勃英 《计算数学》2001,23(2):231-238
1.引言 偏微分方程的近似解法一直是数值计算的重要内容之一。随着计算机的发展,各种实用的新方法也不断涌现.本文在再生核空间H (D)中给出二阶偏微分方程边值问题解析形式的级数解,该级数解具有如下特点:1.级数截断就可直接得到解析数值解;2.解析数值解的误差在空间范数意义下单调下降. 设 D=[a, b] x [c, d]是 R2中的任一矩形域, Г为边界,0,u(x,y)∈L2(D)且是实的绝对连续函数,中规定内积如下: 范数定义为: 山中已证明码(利是一个再生核函数空间,其再生校函数研X,认(,…表达式…  相似文献   

4.
任意变系数微分方程的精确解析法   总被引:7,自引:6,他引:1  
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.  相似文献   

5.
W^12[a,b]空间中线性变系数常微分方程组的精确解   总被引:5,自引:0,他引:5  
该文利用再生核空间的技巧,在W^12「a,b」空间中给出了微分方程组:{u′i(x)+∑nj=1aij(x)uj(x)=fi(x)ui(a)=u^(0)ii=1,2,…,n。的精确解,利用精确解给出了便于用计算机计算的近似解。  相似文献   

6.
将基本解方法推广到二阶和四阶椭圆型偏微分方程的对称问题,在边界上不需要处理奇异积分.通过坐标变换,将一般二阶和四阶椭圆型偏微分方程化为目前研究较为成熟的调和或双调和方程.再根据镜像法构造出适合对称条件的基本解函数,简化了计算,且不影响计算的精度.通过数值计算结果可以看出,利用镜像技术构造出的基本解,前期准备数据少,可保持精度,是一种有效的数值方法.  相似文献   

7.
该文分析了扩展的一般线性方法关于Banach 空间中一类时滞积分微分方程数值解的可解性, 给出了其方法的解的存在唯一性判据, 并探讨了其Newton迭代解的性态. 所获结果可应用于扩展的Runge-Kutta方法和扩展的线性多步方法等.  相似文献   

8.
本文研究了一类非线性问题解分支在二重极限点附近的情况,并且研究了这类问题的有限维近似。本文的结果可以用于非线性偏微分方程的数值解法的理论研究。  相似文献   

9.
该文定义了一个再生核空间W_2~2(*),在其中讨论了积分-微分方程解的存在唯一性,给出了积分-微分方程一个定解问题的精确解的表达式及由精确解得出近似解的性质.  相似文献   

10.
主要研究了一类带有多点边值条件的非线性三阶微分方程的求解方法.利用迭代技巧和再生核(RKM)理论相结合来求解此类问题,同时给出了一些算例来说明方法的有效性.  相似文献   

11.
The time-dependent differential equations of elasticity for 2D quasicrystals with general structure of anisotropy (dodecagonal, octagonal, decagonal, pentagonal, hexagonal, triclinic) are considered in the paper. These equations are written in the form of a vector partial differential equation of the second order with symmetric matrix coefficients. The fundamental solution (matrix) is defined for this vector partial differential equation. A new method of the numerical computation of values of the fundamental solution is suggested. This method consists of the following: the Fourier transform with respect to space variables is applied to vector equation for the fundamental solution. The obtained vector ordinary differential equation has matrix coefficients depending on Fourier parameters. Using the matrix computations a solution of the vector ordinary differential equation is numerically computed. Finally, applying the inverse Fourier transform numerically we find the values of the fundamental solution. Computational examples confirm the robustness of the suggested method for 2D quasicrystals with arbitrary type of anisotropy.  相似文献   

12.
This article is concerned with monotone iterative methods for numerical solutions of a coupled system of a first‐order partial differential equation and an ordinary differential equation which arises from fast‐igniting catalytic converters in automobile engineering. The monotone iterative scheme yields a straightforward marching process for the corresponding discrete system by the finite‐difference method, and it gives not only a computational algorithm for numerical solutions of the problem but also the existence and uniqueness of a finite‐difference solution. Particular attention is given to the “finite‐time” blow‐up property of the solution. In terms of minimal sequence of the monotone iterations, some necessary and sufficient conditions for the blow‐up solution are obtained. Also given is the convergence of the finite‐difference solution to the continuous solution as the mesh size tends to zero. Numerical results of the problem, including a case where the continuous solution is explicitly known, are presented and are compared with the known solution. Special attention is devoted to the computation of the blow‐up time and the critical value of a physical parameter which determines the global existence and the blow‐up property of the solution. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013  相似文献   

13.
研究了层流状态下管道人口压力突然升高引起的水力瞬变过程,建立了瞬态压力分布的偏微分方程和初边值条件,用分离变量法求得了压力的理论解.根据压力和流量问的约束关系,得到了关于流量的偏微分方程和初边值条件.用分离变量求得了瞬变过程流量分布理论解.最后,用特征线法(MOC)对该问题进行了数值求解,理论解和数值解吻合很好.  相似文献   

14.
The variational iterative method is revisited for initial-value problems in ordinary or partial differential equation. A distributional characterization of the Lagrange multiplier - the keystone of the method - is proposed, that may be interpreted as a retarded Green function. Such a formulation makes possible the simplification of the iteration formula into a Picard iterative scheme, and facilitates the convergence analysis. The approximate analytical solution of a nonlinear Klein-Gordon equation with inhomogeneous initial data is proposed.  相似文献   

15.
This article considers the problem of building absolutely minimizing Lipschitz extensions to a given function. These extensions can be characterized as being the solution of a degenerate elliptic partial differential equation, the ``infinity Laplacian', for which there exist unique viscosity solutions.

A convergent difference scheme for the infinity Laplacian equation is introduced, which arises by minimizing the discrete Lipschitz constant of the solution at every grid point. Existence and uniqueness of solutions to the scheme is shown directly. Solutions are also shown to satisfy a discrete comparison principle.

Solutions are computed using an explicit iterative scheme which is equivalent to solving the parabolic version of the equation.

  相似文献   


16.
We consider the modified nodal cubic spline collocation method for a general, variable coefficient, second order partial differential equation in the unit square with the solution subject to the homogeneous Dirichlet boundary conditions. The bicubic spline approximate solution satisfies both the Dirichlet boundary conditions and a perturbed partial differential equation at the nodes of a uniform partition of the square. We prove existence and uniqueness of the approximate solution and derive an optimal fourth order maximum norm error bound. The resulting linear system is solved efficiently by a preconditioned iterative method. Numerical results confirm the expected convergence rates. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011  相似文献   

17.
一类非线性算子方程的迭代求解(英)   总被引:2,自引:1,他引:1  
利用锥理论和半序方法讨论一类非线性算子方程x=Ax的迭代求解问题,得到解的存在唯一性定理,并给出其应用.  相似文献   

18.
In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.  相似文献   

19.
Surface reconstruction from scattered data is an important problem in such areas as reverse engineering and computer aided design.In solving partial differential equations derived from surface reconstruction problems,level-set method has been successfully used.We present in this paper a theoretical analysis on the existence and uniqueness of the solution of a partial differential equation derived from a model of surface reconstruction using the level-set approach.We give the uniqueness analysis of the cl...  相似文献   

20.
提出一种求解线性矩阵方程AX+XB=C双对称解的迭代法.该算法能够自动地判断解的情况,并在方程相容时得到方程的双对称解,在方程不相容时得到方程的最小二乘双对称解.对任意的初始矩阵,在没有舍入误差的情况下,经过有限步迭代得到问题的一个双对称解.若取特殊的初始矩阵,则可以得到问题的极小范数双对称解,从而巧妙地解决了对给定矩...  相似文献   

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