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Poisson积分方程 Galerkin解的外推法(英文) 被引量:2
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作者 刘经洪 李小安 《数学理论与应用》 2002年第1期68-71,共4页
本文讨论 Poisson积分方程 Galerkin解的外推法 。
关键词 Poisson积分方程 galerkin解 有限元 外推法
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旋转椭圆截面螺旋管道内粘性流动的Galerkin解 被引量:1
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作者 张明侃 沈新荣 +1 位作者 麻剑锋 章本照 《自然科学进展》 北大核心 2005年第8期923-929,共7页
对旋转椭圆截面螺旋管道的不可压缩充分发展层流流动方程采用Galerkin方法求解,获得近似分析解.讨论了参数变化时二次流动和轴向速度的变化.结果表明流动结构与旋转、曲率、挠率和截面形状等参数有关.
关键词 旋转螺旋管道 椭圆截面 galerkin方法 galerkin解 螺旋管道 粘性流动 旋转 流动方程 充分发展 不可压缩
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Fredholm积-微分方程Galerkin解的加速收敛分析
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作者 胡齐芽 《系统科学与数学》 CSCD 北大核心 1997年第1期14-18,共5页
本文对一般形式的线性Fredholm积-微分方程推导出迭代Galerkin解及其导数的渐近展式,从而得到了迭代解的外推估计,同时还获得了理想的校正结果.
关键词 galerkin解 积分微分方程 数值 收敛性 迭代
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一类边值问题的Galerkin广义解
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作者 柯云泉 鲁圣洁 《绍兴文理学院学报(自然科学版)》 2002年第3期15-19,共5页
给出一类三维偏微分方程边值问题,构造相应变分问题,讨论边值问题的Galerkin广义解。
关键词 边值问题 变分问题 galerkin广义 存在性 三维偏微分方程 可微函数
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基于边界元方法的边值问题数值解的外推 被引量:1
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作者 刘经洪 朱起定 《吉首大学学报(自然科学版)》 CAS 2005年第2期5-8,共4页
利用边界元方法求解椭圆边值问题,并通过Poisson积分方程的Galerkin解讨论了这种方程的外推算法,进而对边值问题的数值解获得了O(h3)精度的外推结果.
关键词 外推 边界元方法 Poisson积分方程 galerkin解
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一类耦合的KdV型方程的周期解
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作者 丁丽娟 魏公明 《上海理工大学学报》 CAS 北大核心 2013年第6期516-522,共7页
讨论了一类耦合的KdV方程在一定条件下周期解的存在性.利用Sobolev不等式,给出了此方程解的估计以及它们的一二三阶导数的估计,然后根据Galerkin近似解及其先验估计,得到了耦合KdV方程弱解的局部存在性.
关键词 KDV方程 周期 galerkin近似 先验估计
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二维环面上带约束的非自治二维随机Navier-Stokes方程的鞅解
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作者 吕海冲 李晓军 《河北师范大学学报(自然科学版)》 CAS 2023年第6期558-568,共11页
研究二维环面上带L2-范数约束的非自治随机Navier-Stokes方程鞅解的存在性.首先,利用随机外力中驱动算子的斜对称性和Galerkin近似解序列的一致估计,得到近似解分布的tight紧性.其次,构造新的概率空间及定义于其上的新随机过程,使得近... 研究二维环面上带L2-范数约束的非自治随机Navier-Stokes方程鞅解的存在性.首先,利用随机外力中驱动算子的斜对称性和Galerkin近似解序列的一致估计,得到近似解分布的tight紧性.其次,构造新的概率空间及定义于其上的新随机过程,使得近似解于其上收敛到该随机过程.最后,证明所得新随机过程是原方程的解.同时,得到所得鞅解沿样本轨道唯一,进而得到原方程强解的存在性. 展开更多
关键词 NAVIER-STOKES方程 galerkin近似
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三维Stokes近似系统弱解的全局存在性
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作者 郭蒙 郭志召 《高师理科学刊》 2011年第1期22-25,共4页
研究了三维有界光滑区域上的Stokes近似系统弱解的全局存在性.利用Galerkin格式构造逼近方程组,进而通过取极限得到原系统的解,证明了三维Stokes近似系统弱解的全局存在性.
关键词 三维Stokes近似系统 全局弱 galerkin逼近
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Burgers方程的小波近似惯性流形及数值分析
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作者 田立新 许伯强 刘曾荣 《应用数学和力学》 EI CSCD 北大核心 2002年第10期1013-1024,共12页
研究Burgers方程小波基下小波近似惯性流形的存在性 ,并作低阶多分辨分析下的数值分析 。
关键词 BURGERS方程 小波近似惯性流形 数值分析 小波galerkin解 无穷维动力系统
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轴向运动薄板的自由振动分析 被引量:4
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作者 张芳芳 随岁寒 +2 位作者 晋会杰 庞静艺 王浩然 《井冈山大学学报(自然科学版)》 2022年第4期70-77,共8页
首次利用解析法求解了轴向运动薄板的自由振动问题,并对解析结果进行了Galerkin法验证。基于Kirchhoff薄板理论,根据Hamilton原理推导轴向运动薄板自由振动的控制方程,分别采用解析法和Galerkin法求解控制方程,得到了四边简支条件下系... 首次利用解析法求解了轴向运动薄板的自由振动问题,并对解析结果进行了Galerkin法验证。基于Kirchhoff薄板理论,根据Hamilton原理推导轴向运动薄板自由振动的控制方程,分别采用解析法和Galerkin法求解控制方程,得到了四边简支条件下系统固有频率的解析解和数值解。同时,得到了第一阶临界速度的解析表达式。轴向速度为零时,对比了解析解、Galerkin数值解和ANSYS软件解,三种方法所得结果高度吻合。随后对比了不同速度条件下的解析解与Galerkin解,分析了预应力与临界速度的关系。发现在低速条件下离心力是影响系统振动的主要因素,科氏力影响可忽略;第一阶固有频率的解析解仅适用于低速条件,高阶固有频率的解析解适用的速度范围大。 展开更多
关键词 轴向运动薄板 自由振动 galerkin解
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A Characterization of Existence of Global Solutions for Some Fourth-order Wave Equations
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作者 陈勇明 杨晗 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第1期109-114,共6页
The initial boundary value problem for the fourth-order wave equation u_(tt)+△~2u+u=|u|^(p-1)u is considered.The existence and uniqueness of global weak solutions is obtained by using the Galerkin method and the conc... The initial boundary value problem for the fourth-order wave equation u_(tt)+△~2u+u=|u|^(p-1)u is considered.The existence and uniqueness of global weak solutions is obtained by using the Galerkin method and the concept of stable set due to Sattinger. 展开更多
关键词 wave equation global solutions galerkin method potential well
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Brake Subharmonic Solutions of Subquadratic Hamiltonian Systems 被引量:2
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作者 Chong LI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第3期405-418,共14页
The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z(t) = JVH... The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z(t) = JVH(t, z(t)), where H(t, z) = 1/2(B(t)z, z) + H(t, z), B(t) is a semipositive symmetric continuous matrix and H is unbounded and not uniformly coercive. It is proved that when the positive integers j and k satisfy the certain conditions, there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct. 展开更多
关键词 Brake subharmonic solution L-Maslov type index Hamiltonian systems
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Attractors for a von Karman equation with memory 被引量:1
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作者 PARK SunHye 《Science China Mathematics》 SCIE CSCD 2015年第12期2505-2516,共12页
In this paper a von Karman equation with memory,utt + α?2u- γ?utt- integral from n=-∞ to t μ(t- s)?2u(s)ds = [u, F(u)] + h is considered. This equation was considered by several authors. Existing results are mainl... In this paper a von Karman equation with memory,utt + α?2u- γ?utt- integral from n=-∞ to t μ(t- s)?2u(s)ds = [u, F(u)] + h is considered. This equation was considered by several authors. Existing results are mainly devoted to global existence and energy decay. However, the existence of attractors has not yet been considered. Thus, we prove the existence and uniqueness of solutions by using Galerkin method, and then show the existence of a finitedimensional global attractor. 展开更多
关键词 von Karman equation global attractor VISCOELASTICITY MEMORY
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Analytical Solutions for the Two-Dimensional Gross-Pitaevskii Equation with a Harmonic Trap 被引量:1
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作者 石玉仁 王雪玲 +2 位作者 王光辉 刘丛波 杨红娟 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第3期273-278,共6页
Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used ... Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential. The approximate analytical solutions are obtained successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is not too strong. 展开更多
关键词 Gross-Pitaevskii equation homotopy analysis method analytical solution
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On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schr¨odinger Equation for Interdiffused Quantum Wells and Quantum Wires
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作者 D.B.Topalovi V.V.Arsoski +3 位作者 S.Pavlovic N.A.Cukaric M.Z.Tadic F.M.Peeters 《Communications in Theoretical Physics》 SCIE CAS CSCD 2016年第1期105-113,共9页
We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schr¨odinger equation.The accuracy of the solution is explored as it varies with the range of the numerical domai... We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schr¨odinger equation.The accuracy of the solution is explored as it varies with the range of the numerical domain.The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires.Also,the model of a linear harmonic oscillator is considered for comparison reasons.It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range,which is thus considered to be optimal.This range is found to depend on the number of mesh nodes N approximately as α_0 log_e^(α1)(α_2N),where the values of the constants α_0,α_1,and α_2are determined by fitting the numerical data.And the optimal range is found to be a weak function of the diffusion length.Moreover,it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schr¨odinger equation. 展开更多
关键词 intermixing quantum well quantum wire Schrodinger equation finite element adaptive
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A second order finite difference-spectral method for space fractional diffusion equations 被引量:4
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作者 HUANG JianFei NIE NingMing TANG YiFa 《Science China Mathematics》 SCIE 2014年第6期1303-1317,共15页
A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The s... A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The stability and error estimates of the temporal semidiscrete scheme are rigorously discussed,and the convergence order of the proposed method is proved to be O(τ2+Nα-m)in L2-norm,whereτ,N,αand m are the time step size,polynomial degree,fractional derivative index and regularity of the exact solution,respectively.Numerical experiments are carried out to demonstrate the theoretical analysis. 展开更多
关键词 space fractional diffusion equation Crank-Nicolson scheme spectral method STABILITY conver-gence
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On the Numerical Solution to a Nonlinear Wave Equation Associated with the First Painlev Equation:an Operator-Splitting Approach
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作者 Roland GLOWINSKI Annalisa QUAINI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2013年第2期237-254,共18页
The main goal of this article is to discuss the numerical solution to a nonlinear wave equation associated with the first of the celebrated Painlevd transcendent ordinary differential equations. In order to solve nume... The main goal of this article is to discuss the numerical solution to a nonlinear wave equation associated with the first of the celebrated Painlevd transcendent ordinary differential equations. In order to solve numerically the above equation, whose solutions blow up in finite time, the authors advocate a numerical methodology based on the Strang's symmetrized operator-splitting scheme. With this approach, one can decouple nonlinearity and differential operators, leading to the alternate solution at every time step of the equation as follows: (i) The first Painlevd ordinary differential equation, (ii) a linear wave equation with a constant coefficient. Assuming that the space dimension is two, the authors consider a fully discrete variant of the above scheme, where the space-time discretization of the linear wave equation sub-steps is achieved via a Galerkin/finite element space approximation combined with a second order accurate centered time discretization scheme. To handle the nonlinear sub-steps, a second order accurate centered explicit time discretization scheme with adaptively variable time step is used, in order to follow accurately the fast dynamic of the solution before it blows up. The results of numerical experiments are presented for different coefficients and boundary conditions. They show that the above methodology is robust and describes fairly accurately the evolution of a rather "violent" phenomenon. 展开更多
关键词 Painlevd equation Nonlinear wave equation Blow-up solution Operator-SDlitting
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