双比例延迟微分方程配置法的可达阶

近几十年来,随着延迟微分方程广泛应用于变最测试、信号传递、机械化工、生命科学及经济管理系统等实际中,人们对此类方程的数值计算要求越来越高．     

多滞量积分方程基于高阶插值的分步配置方法

1．引言考虑多滞量Volterra积分方程其中常数假定已知函数R在定义域内连续，以保证方程（1.1）存在唯一解形如（1．1）的Volterra延滞积分方程常出现在物理问题和生物模型中［2］．由于“滞量”的影响，对其作理论分析和数值研究均比“古典”的Volterra积分方程更为困难．近来人们对Volterra延滞积分方程的数值求解越来越感兴趣[3，4]，但目前的工作基本上只限于单滞量的情形：并采用所谓的“约束”网格（即要求步长人整除一，且假定T是，的整数倍（否则，应在更大的区间上求解），以保证数值解在结点集上具有理想的收敛率．显然，这些限…     

非线性积分方程迭代配置法的渐近展开及其外推

非线性积分方程迭代配置法的渐近展开及其外推韩国强（华南理工大学计算机工程与科学系）ＡＳＹＭＰＴＯＴＩＣＥＲＲＯＲＥＸＭＮＳＩＯＮＳＡＮＤＥＸＴＲＡＰＯＬＡＴＩＯＮＦＯＲＴＨＥＩＴＥＲＡＴＥＤＣＯＬＬＯＣＡＴＩＯＮＭＥＴＨＯＤＳＯＦＮＯＮＬＩＮＥＡＲＩ...     

SPECTRAL ANALYSIS OF THE FIRST-ORDER HERMITE CUBIC SPLINE COLLOCATION DIFFERENTIATION MATRICES

It has been observed numerically in [1] that, under certain conditions, all eigenvalues of the first-order Hermite cubic spline collocation differentiation matrices with unsymmetrical collocation points lie in one of the half complex planes. In this paper, we provide a theoretical proof for this spectral result.     

Hammerstein型弱奇异积分方程的β-多项式配置方法

1．引言对VOlterra弱奇异积分方程和积一微分方程之配置方法已有不少文章讨论［1－6］．由于其解在左端点处的非光滑性[3]并要得到m-1次多项式配置解的最优收敛率。，需采用所谓的等级网格．早期M作［1,2］是将等级指数r取为1，a表征核（t—s）ak（t，8）的奇异程度），但...     

高维非线性Schrdinger方程的Fourier谱方法

其中i=(-1)(1/2),△为Laplace算子,q(·)为实变量实值函数,u_0(x)和u(x,t)分别为关于x以2π为周期的已知和未知复值函数,J=(0,T](T>0),β为一实常数,e_j为R~m的第j个单位向量,x=(x_1,…,x_m)∈R~m. 方程(1.1)在非线性光学、等离子体物理、流体动力学及非相对论量子场论中用得很     

A COLLOCATION METHOD FOR THE CONDUCTIVITY PROBLEM WITH DISCONTINUOUS COEFFICIENT

In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the 7 is a piecewise constant function. By the integral representation formula of the solution of the conductivity equation on the boundary and interface, the boundary integral equations are obtained. We discuss the properties of these integral equations and propose a collocation method for solving these boundary integral equations. Both the theoretical analysis and the error analysis are presented and a numerical example is given.     

非线性第二类Volterra积分方程的Chebyshev谱配置法

我们在参考了相关文献的基础上,考察了一类非线性Volterra积分方程的Chebyshev谱配置法.方法中,我们将该类非线性方程转化为两个方程进行数值逼近.我们选择N阶Chebyshev Gauss-Lobatto点作为配置点,对积分项用N阶高斯数值积分公式逼近.收敛性分析结果表明数值误差的收敛阶为N^（1/2）-m,其中m是已知函数最高连续导数的阶数.我们也开展数值实验证实这一理论分析结果.     

IMPLICITY LINEAR COLLOCATION METHOD AND ITERATED IMPLICITY LINEAR COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF HAMMERSTEIN FREDHOLM INTEGRAL EQUATIONS ON 2D IRREGULAR DOMAINS

In this work, we adapt and compare implicity linear collocation method and iterated implicity linear collocation method for solving nonlinear two dimensional Fredholm integral equations of Hammerstein type using IMQ-RBFs on a non-rectangular domain. IMQs show to be the most promising RBFs for this kind of equations. The proposed methods are mesh-free and they are independent of the geometry of domain. Convergence analysis of the proposed methods together with some benchmark examples is provided which support their reliability and numerical stability.     

THE PREDICTION-CORRECTION LEGENDRE COLLOCATION METHOD FOR NONLINEAR EVOLUTIONARY PROBLEMS

The initial-boundary value problem of Burgers equation is considered. A prediction-correction Legendre collocation scheme is presented, which is easy to be performed. Its numerical solution possesses the accuracy of second-order in time and higher order in space. Numerical results are reported, which show the high accuracy of this approach. The techniques used in this paper are also applicable to other nonlinear evolutionary problems.