共查询到19条相似文献,搜索用时 62 毫秒
1.
利用数值求积公式,将三维第一类Fredholm积分方程进行离散,通过引入正则化方法,将离散后的积分方程转化为一离散适定问题,通过广义极小残余算法得到了其数值解.数值模拟结果表明该方法的可行有效性. 相似文献
2.
我们提出和分析了一种求解Stokes方程的数值方法.新方法基于空间上的Legendre谱离散,时间上则采用投影/方向分裂格式.更确切地说,时间离散的出发点是旋度形式的压力校正投影法,在此基础上进一步应用方向分裂法,把速度和压力方程分裂为一系列一维的椭圆型子问题.然后生成的这些一维子问题用Legendre谱方法进行空间离散.另外,我们证明了全离散格式的稳定性.一些数值实验验证了收敛性和方法的有效性. 相似文献
3.
基于透射边界条件的高阶离散型角点条件 总被引:2,自引:0,他引:2
对波动方程的数值模拟中,在有限区域建立吸收边界条件,其中对区域角点的处理是一个很重要的问题.随着吸收边界条件阶数的提高,与之匹配的角点条件也越难建立.MTF是一种离散型吸收边界条件.在此,对于二维问题,基于MTF建立离散型高阶角点条件,对计算区域角点处理时,在区域对角线方向上建立N阶MTF公式.问题也可推广到三维.数值结果证实了我们的猜测. 相似文献
4.
第一类弱奇异核Fredholm积分方程由于奇异及本质的不适定性,给求解带来很大难度.本文首先利用克雷斯变换将方程转化,并对转化后的方程进行高斯一勒让德离散,得到一离散不适定的线性方程组,结合正则化方法对该类问题进行数值求解.最后给出了数值模拟,验证了本文方法的可行性及有效性. 相似文献
5.
本文分别基于原始变分形式与对偶混合变分形式,对一类单边约束问题进行了数值求解,提出了求解离散对偶混合变分问题的Uzawa型算法,并用数值例子验证了算法的有效性. 相似文献
6.
本文构造了三维涡度方程双向周期问题的Fourier拟谱─差分格式,其数值解满足半离散守恒律.文中分析了格式的广义稳定性和收敛性.数值例子表明这类格式的优越性. 相似文献
7.
多体系统动力学微分/代数方程组的一类新的数值分析方法 总被引:3,自引:0,他引:3
本文讨论了多体系统动力学微分/代数混合方程组的数值离散问题.首先把参数t并入广义坐标讨论,简化了方程组及其隐含条件的结构,并将其化为指标1的方程组.然后利用方程组的特殊结构,引入一种局部离散技巧并构造了相应的算法.算法结构紧凑,易于编程,具有较高的计算效率和良好的数值性态,且其形式适合于各种数值积分方法的的实施.文末给出了具体算例. 相似文献
8.
9.
本文利用Thkhonov正则化方法讨论了带有噪声离散数据的周期函数的数值微分问题,证明了该方法存在唯一的三次周期样条函数解,并给出了其误差估计,而且从理论和数值例子说明了此方法的有效性. 相似文献
10.
非线性整数规划的一个近似算法 总被引:14,自引:1,他引:13
利用连续总体优化填充函数法的思想,本文设计了非线性整数规划的一个近似算法.首先,给出了非线性整数规划问题离散局部极小解的定义,设计了找离散局部极小解的局部搜索算法;其次,用所设计的局部搜索算法极小化填充函数来找比当前离散局部极小解好的解.本文的近似算法是直接法,且与连续总体优化的填充函数法相比,本文填充函数中的参数易于选取.数值试验表明,本文的近似算法是有效的. 相似文献
11.
数值模拟混溶驱动问题的迎风格式及理论分析 总被引:9,自引:2,他引:7
梁栋 《高校应用数学学报(A辑)》1994,(2):118-127
本文提出数据模拟混溶驱动问题的一类广义迎风格式,严格证明了其满足离散极值原理和离散质量守恒原理,并获得收敛性定理,对模型问题的试算,得到令人满意的数值结果。 相似文献
12.
本文给出Steklov特征值问题基于Legendre-Galerkin逼近的一种有效的谱方法.首先利用Legendre多项式构造了一组适当的基函数使得离散变分形式中的矩阵是稀疏的,然后推导了2维及3维情形下离散变分形式基于张量积的矩阵形式,由此可以快速地计算出离散的特征值和特征向量.文章还给出了误差分析和数值试验,数值结果表明本文提出的方法是稳定和有效的. 相似文献
13.
Michael Hinze 《Numerische Mathematik》1996,73(1):95-118
Summary.
This work is concerned with the approximation and
the numerical
computation of polygonal minimal surfaces in
.
Polygonal minimal surfaces correspond to the
critical points of
Shiffman's function
. Since this function is analytic,
polygonal minimal surfaces can be characterized by
means of the second
derivative of .
We present a finite element
approximation of
quasiminimal surfaces together with an error
estimate. In this way we
obtain discrete approximations
of
and of
. In particular we prove that the
discrete functions
converge uniformly on certain compact subsets. This
will be the main
tool for proving existence and convergence of
discrete minimal
surfaces in neighbourhoods of non-degenerate
minimal surfaces. In the
numerical part of this paper we compute numerical
approximations of
polygonal minimal surfaces by use of Newton's
method applied to .
Received October 27, 1994 相似文献
14.
复杂系统的离散质量生存决策 总被引:2,自引:0,他引:2
在复杂系统的质量生存交互决策中,引入了最大质量生存函数W*的概念.为得到W*的数值计算方法,本文系统地研究了离散质量生存(交互)决策和最大离散质量生存函数,推导出最大离散质量生存函数的递归算法,最后用离散算法获得最大Q-生存函数W*的两类离散近似解:有限近似离散近似解和加厚法离散近似解,并给出近似解的收敛性证明. 相似文献
15.
Jing Wen Jian Su Yinnian He Hongbin Chen 《Numerical Methods for Partial Differential Equations》2021,37(1):383-405
In this paper, a semi‐discrete scheme and a fully discrete scheme of the Stokes‐Biot model are proposed, and we analyze the semi‐discrete scheme in detail. First of all, we prove the existence and uniqueness of the semi‐discrete scheme, and a‐priori error estimates are derived. Then, we present the same conclusions for the fully discrete scheme. Finally, under both matching and non‐matching meshes some numerical tests are given to validate the analysis of convergence, which well support the theoretical results. 相似文献
16.
C. Besse M. Ehrhardt I. Lacroix‐Violet 《Numerical Methods for Partial Differential Equations》2016,32(5):1455-1484
We consider the derivation of continuous and fully discrete artificial boundary conditions for the linearized Korteweg–de Vries equation. We show that we can obtain them for any constant velocities and any dispersion. The discrete artificial boundary conditions are provided for two different numerical schemes. In both continuous and discrete case, the boundary conditions are nonlocal with respect to time variable. We propose fast evaluations of discrete convolutions. We present various numerical tests which show the effectiveness of the artificial boundary conditions.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1455–1484, 2016 相似文献
17.
Guo-Fu Yu 《Journal of Difference Equations and Applications》2019,25(3):408-429
In this paper, we study the generalized coupled integrable dispersionless (GCID) equations and construct two integrable discrete analogues including a semi-discrete system and a full-discrete one. The results are based on the relations among the GCID equations, the sine-Gordon equation and the two-dimensional Toda lattice equation. We also present the N-soliton solutions to the semi-discrete and fully discrete systems in the form of Casorati determinant. In the continuous limit, we show that the fully discrete GCID equations converge to the semi-discrete GCID equations, then further to the continuous GCID equations. By using the integrable semi-discrete system, we design two numerical schemes to the GCID equations and carry out several numerical experiments with solitons and breather solutions. 相似文献
18.
19.
In this Note we prove a discrete version of the classical Ingham inequality for nonharmonic Fourier series whose exponents satisfy a gap condition. Time integrals are replaced by discrete sums on a discrete mesh. We prove that, as the mesh becomes finer and finer the limit of the discrete Ingham inequality is the classical continuous one. This analysis is partially motivated by control-theoretical applications. As an application we analyze the control/observation properties of numerical approximation schemes of the 1-d wave equation. The discrete Ingham inequality provides observability and controllability results which are uniform with respect to the mesh size in suitable classes of numerical solutions in which the high frequency components have been filtered. To cite this article: M. Negreanu, E. Zuazua, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献