一阶混合型方程组的间断边值问题

本文论讨单连通区域上一阶线性混合型(椭圆—双曲型)方程组的间断边值问题.我们首先给出混合型方程组特别是最简单的混合型方程组解的表示式,然后使用逐次逼近法,证明上述边值问题解的存在性与唯一性.由以上结果,可导出A.V.Bitsadze所得的Lavrent’ev-Bitsadze方程u     

NUMERICAL SOLUTIONS OF DISCONTINUOUS BOUNDARY VALUE PROBLEMS FOR GENERAL ELLIPTIC COMPLEX EQUATIONS OF FIRST ORDER

1Formulati0nofDiscontinuousBoundaryValueProblemsLetDbeanN 1-connectedb0undeddomaininthez=x iy-planeCwiththeboundaryFEC:(0相似文献   

HOMOTOPY CONTINUATION METHODS FOR STOCHASTIC TWO-POINT BOUNDARY VALUE PROBLEMS DRIVEN BY ADDITIVE NOISES

In this paper the homotopy continuation method for stochastic two-point boundary value problems driven by additive noises is studied. The existence of the solution of the homotopy equation is proved. Numerical schemes are constructed and error estimates are obtained. Numerical experiments demonstrate the effectiveness of the homotopy continu- ation method over other commonly used methods such as the shooting method.     

THE DEFECT ITERATION OF THE FINITE ELEMENT FOR ELLIPTIC BOUNDARY VALUE PROBLEMS AND PETROV-GALERKIN APPROXIMATION

1.IntroductionFranketc.of.[l]establishedtheiterateddefectcorrectionschemeforfiniteelemelltofellipticboundaryproblems.FOrlinearellipticboundaryvalueproblem[2--5]havediscllssedtheefficiencyoftheschemebyusillgsuperconvergenceandasymptoticexpansion"lidertheco…     

解一类半线性外边值问题的自然边界元与有限元耦合法

In this paper, we combine a finite element approach with the natural boundary element method to stduy the weak solvability and Galerkin approximations of a class of semilinear exterior boundary value problems. Our analysis is mainly based on the variational formulation with constraints. We discuss the error estimate of the finite element solution and obtain the asymptotic rate of convergence O（h^n) Finally, we also give two numerical examples.     

一类离散m点边值问题正解的存在性与多重性

本文运用锥上的不动点理论,得到了一类离散多点边值问题的一个正解及两个正 解存在性.     

n阶非线性常微分方程组边值问题的正解

运用不动点指数理论,研究以下$n$阶非线性常微分方程组边值问题正解的存在性和多重正解的存在性\[\left\{\ay\begin{array}{l}-u^{(n)}=f_1(x,u,v),\q-v^{(n)}=f_2(x,u,v),\\[2mm]u^{(i)}(0)=u^{(p)}(1)= v^{(i)}(0)=v^{(p)}(1)=0.\end{array}\right. \] 这里$n\geq 2$, $i = 0,1,2,\cdots,n-2$, $p \in \{1,2,\cdots,n-1\}$, $f_i\in C([0,1]\times\mathbb R^+\times\mathbb R^+,\mathbb R^+)~(i=1,2)$. 用凹函数刻画非线性项$f_1,f_2$的耦合行为, 因而非线性项 $f_i(i=1,2)$ 既可以都是超线性的, 也可以都是次线性的,还可以是混合非线性的(即其中一个是超线性的, 另一个是次线性的).     

ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson's extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson's extrapolation.     

BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF NONLINEAR SECOND ORDER DIFFERENTIAL DFFERENCE EQUATIONS

The author studies the boundary value problems for systems of nonlinear second order differential difference equations and adopts a new-type Nagumo condition,in whichthe control function is a vector-valued function of several variables and which can guarantee simultaneoulsy and easily finding a priori bounds of each component of the derivatives of the solutions,Under this new-type Nagumo condition the existence results of solutions are proved by means of differential inequality technique.     

伪抛物型复方程的Riemann─Hilbert初边值问题的可解性及其近似解的误差估计

本文使用参数开拓法证明了非线性伪抛物型复方程在多连通区域上的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ初边值问题的可解性，并对近似解作出了误差估计。     

关于2n阶常微分方程两点边值问题解的存在性与唯一性

本文利用Leray－Schauder度理论建立了一类2n阶非线性常微分方程两点边值问题解的存在性与唯一性定理，以及利用Fredholm择一原理与Fourier展式，建立了一类2n阶线性常微分方程两点边值问题解的存在性唯一性定理．     

Banach 空间中奇异积分-微分方程边值问题多解的存在性

通过建立一个特殊的锥,运用锥拉伸与锥压缩不动点定理,获得了Banach空间中一类非线性混合型奇异积分-微分方程边值问题多解的存在性．     

二维抛物型方程初边值问题的高阶差分边界元法及误差估计

本文讨论二维抛物型方程初边值问题的求解问题，提出了一种差分与边界元耦合的高阶求解方法，并给出了先验误差估计。     

关于—类三阶混合型方程和变系数双曲型方程的边值问题

本文先扼要介绍一类三阶双曲抛物混合型偏微分方程的边值问题，然后讨论了与之有关的一类变系数三阶双曲型方程以特征线为支柱的边值问题，得到了有唯一解时此变系数应满足的充分必要条件。     

非共振奇异超线性边值问题正解存在的充分必要条件

本文研究非共振奇异超线性边值问题正解的存在性,利用锥上的不动点定理给出了非共振奇异超线性边值问题有C1[0,1]正解存在的充分必要条件.     

微分、差分方程的机械化方法

介绍了微分与差分方程机械化方法研究若干最新进展.主要结果包括: 微分、差分方程的特征列理论与算法,微分、差分方程系统的分解算法以及微分、差分方程解析解求解算法.     

一类离散$\mbox{\boldmath $m$}$点边值问题正解的存在性与多重性

本文运用锥上的不动点理论，得到了一类离散多点边值问题的一个正解及两个正解存在性.     

MULTIGRID ALGORITHM FOR THE COUPLING SYSTEM OF NATURAL BOUNDARY ELEMENT METHOD AND FINITE ELEMENT METHOD FOR UNBOUNDED DOMAIN PROBLEMS

In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported.     

A NEW PRECONDITIONING STRATEGY FOR SOLVING A CLASS OF TIME-DEPENDENT PDE-CONSTRAINED OPTIMIZATION PROBLEMS

In this paper, by exploiting the special block and sparse structure of the coefficient matrix, we present a new preconditioning strategy for solving large sparse linear systems arising in the time-dependent distributed control problem involving the heat equation with two different functions. First a natural order-reduction is performed, and then the reduced- order linear system of equations is solved by the preconditioned MINRES algorithm with a new preconditioning techniques. The spectral properties of the preconditioned matrix are analyzed. Numerical results demonstrate that the preconditioning strategy for solving the large sparse systems discretized from the time-dependent problems is more effective for a wide range of mesh sizes and the value of the regularization parameter.