一类一阶常微分方程初值问题的无穷多解性

应用分离变量法,得到了一类一阶微分方程初值问题u′(t)=b(t)f(u(t)),t0,u(0)=0存在无穷多个解的充分必要条件.并给出了全部解.     

显式线性三步二阶方法的稳定性讨论

1 引 言 关于常微分方程初值问题 y′=f(t,y), t∈[t_0,T]R, y(t_0)=y_0, y,f∈R~m,m≥1, (1.1)存在许多数值方法,显式线性多步法,特别是Adams—Bashforth方法,由于其具有计算格式     

常微分方程初值问题的一种改进单步方法

针对一类常微分方程初值问题u'=a(t)u f(u),u(0=α,用Hermite插值积分,获得了一种改进的4阶单步方法,并证明了该格式的稳定性和收敛性,数实实验表明,与4阶Runge-Kutta方法,4阶Gear方法相经,长较大时,该格式仍具有较好的精度。     

一类四阶非线性微分方程两点边值问题的正解

应用锥理论和不动点指数方法,在与相应的线性算子第一特征值有关的条件下,获得了一类四阶非线性常微分方程两点边值问题{-u(4)(t)t=f(t,u(t)),≤t≤1,u(0)=u′(0)=u′(1)=u′″(1)=0正解的存在性.     

Banach空间中微分方程的弱Carathodory解

本文在一般Banach空间中讨论微分方程的初值问题：u＇＝f（t，u），u（0）＝x0．设f（t，u）不连续，仅满足所谓弱Caratheodory条件，但仍证明了初值问题的解可由迭代序列的一致极限得到，并给出了逼近解的迭代序列的误差估计．对周期过值问题得到了类似的结果．     

二阶奇异微分方程边值问题的正解

利用上下解方法研究二阶奇异微分方程u″+f(t,u)=0在边界条件αu(0)-βu′(0)=0,γu(1)+δu′(1)=0下正解的存在性.允许f(t,u)在t=0,1处奇异.     

一类四阶边值问题正解的存在性

讨论了四阶常微分方程边值问题u^(4)=βu″-au=ψ(t)f(u),u(0)=u(1)=u″（0)=u″(1)=0的正解的存在性,利用锥拉伸与锥压缩不动点定理证明了,当f(u)在u=0及u=∞超线性或次线性增长时,该问题至少存在一个正解。     

用椭圆描述的四阶边值问题的两参数非共振条件

该文讨论四阶常微分方程边值问题u(4)=f(t,u,u″),0≤t≤1,u(0)=u(1)=u″(0)=u″(1)=0解的存在性,其中f:[0,1]×R×R→R连续.文中提出了一个保证该问题解存在的两参数非共振条件,该条件是用椭圆描述的.     

Banach空间中四阶边值问题的正解

利用极大值原理,比较定理和增算子不动点定理研究Banach空间中四阶常微分方程两点边值问题{u~((4))(t)=f(t,u(t)),0相似文献   

Banach空间常微分方程的解

在[4]中,S.V.Du和V.Lakshmikantham利用紧型条件证明了必存在单调序列{v_n}和{w_n},一致收敛于Banach空间常微分方程初值问题u′=f(t,u),u(0)=u_0的最大解和最小解。在本文中我们证明了,如果Banach空间是弱序列完备的,则[4]中的紧型条件(这是[4]中的一个主要条件)是可以删掉的。我们还对Banach空间周期边值问题证明了类似的结果。     

Superconvergence of Continuous Finite Elements with Interpolated Coefficients for Initial Value Problems of Nonlinear Ordinary Differential Equation

In this paper, n-degree continuous finite element method with interpolated coefficients for nonlinear initial value problem of ordinary differential equation is introduced and analyzed. An optimal superconvergence u - uh = O（h^n＋2）, n ≥ 2, at （n ＋ 1）-order Lobatto points in each element respectively is proved. Finally the theoretical results are tested by a numerical example.     

抛物方程时间连续有限元全离散格式的超收敛性

利用张量积分解和时间方向单元正交分解,证明了线性抛物型方程的时间连续全离散有限元在单元节点和内部的特征点的超收敛性.并用连续有限元计算了非线性Schrodinger方程,验证了能量的守恒性.计算结果与理论相吻合.     

二维分岔槽道内非牛顿流体流动的有限元分析

本文介绍二维分岔槽道内非牛顿流体流动的有限元分析.采用Galerkin法及混合有限元法,流体看作不可压缩的非牛顿流体,满足Oldyord微分型本构方程.由有限元法形成的非线性代数方程组用连续微分法求解.结果表明有限元法适于分析复杂流场中非牛顿流体的流动.     

A Variational Analysis for the Moving Finite Element Method for Gradient Flows

By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized problem has the same energy dissipation structure as the continuous one. This enables us to do numerical analysis for the stationary solution of a nonlinear reaction diffusion equation using the approximation theory of free-knot piecewise polynomials. We show that under certain conditions the solution obtained by the moving finite element method converges to a local minimizer of the total energy when time goes to infinity. The global minimizer, once it is detected by the discrete scheme, approximates the continuous stationary solution in optimal order. Numerical examples for a linear diffusion equation and a nonlinear Allen-Cahn equation are given to verify the analytical results.     

Strong convergence of an iterative method for pseudo-contractive and monotone mappings

In this paper, we introduce an iterative process which converges strongly to a common element of fixed points of pseudo-contractive mapping and solutions of variational inequality problem for monotone mapping. As a consequence, we provide an iteration scheme which converges strongly to a common element of set of fixed points of finite family continuous pseudo-contractive mappings and solutions set of finite family of variational inequality problems for continuous monotone mappings. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings.     

三维热传导型半导体问题的交替方向特征有限元方法及理论分析

１．引言 三维热传导型半导体器件瞬态问题的数学模型由四个非线性偏微分方程描述 ［１,２］．工程研究中一般考虑绝流边条件,由于绝流条件可以看作一反射条件来处理、为了数值分析方便,我们在此考虑三维周期问题： 其中,　＝［０,１］３,未知函数是电子位势　;电子,空穴浓度ｅ,ｐ;温度函数Ｔ．方程（１,１）－（１.４）中出现的系数均有正的上下界,且是　周期的． ａ＝Ｑ／ε,Ｑ,ε分别表示电子负荷和介电系数,均为正常数．Ｎ（ｘ）是给定的函数．Ｄｓ（ｘ）为扩散系数,μｓ（ｘ）为迁移率,ｓ＝ｅ,Ｐ．Ｒ（ｅ,ｐ,Ｔ）…     

DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR A FORWARD-BACKWARD HEAT EQUATION

A space-time finite element method,discontinuous in time but continuous in space, is studied to solve the nonlinear forward-backward heat equation. A linearized technique is introduced in order to obtain the error estimates of the approximate solutions. And the numerical simulations are given.     

Hybrid Finite Element Method for Two-phase Miscible Displacement in Porous Media

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求解带有非线性边界条件的涡流方程的A-φ解耦有限元格式

本文研究边界条件符合幂指数型非线性关系H × n = n × (|E × n|^α-1E × n)(0 < α ≤ 1)的涡流方程.使用A-φ耦合有限元格式数值求解这类问题具有较高精度,但计算开销大. A-φ解耦有限元计算格式能够在每个时间步上分别求解矢量A和标量φ,以此降低计算规模,提高计算效率.我们证明了解耦格式中解的存在唯一性,并且给出了它的误差估计.最后给出的数值实验证明了本文所提供的解耦算法是稳定和有效的.