Klein-Gordon方程初达值问题的一个新的守恒差分格式

本文对非线性Klein－Gordon（NKG）方程的初边值问题提出了一种新的差分格式,它保持了NKG方程初边值问题的能量守恒．证明了该格式的收敛性和稳定性．特别地,由于该格式是完全隐式的,故对求长时解有着重要的作用．数值计算结果表明该方法计算速度快,精度好．     

Klein—Gordon方程初边值问题的一个新的守恒差分格式

本文对非线性Ｋｌｅｉｎ－Ｇｏｒｄｏｎ（ＮＫＧ）方程的初边值问题提出了一种新的差分格式，它保持了ＮＫＧ方程初边值问题的能量守恒。证明了该格式的收敛性和稳定性。特别地，由于该格式是完全隐式的，故对求长时解有着重要的作用。数值计算结果表明该方法计算速度快，精度好。     

对流扩散方程的数值计算

本文研究了对流扩散方程的一种并行格式.利用一组saul'yev型非对称格式进行二次构造,分别得到了一类并行GE格式和GEL、GER格式;进一步推广,得到绝对稳定的交替分组显式AGE格式,并用数值例子检验AGE格式的数值计算效果.     

一类求解BURGERS方程的LEGENDRE谱格式

本文考虑非稳态Burgers方程的初边值问题,构造了一类Legendre谱计算格式,证明了其收敛性并给出了一些数值试验结果。     

油藏数值模拟中动边值问题的迎风差分格式

考虑了三维油藏数值模拟中的动边值问题,对压力方程,给出中心差分格式;对饱和度方程给出隐式迎风差分格式及修正的迎风差分格式,并证明了格式的收敛性。数值算例与理论结果是一致的。     

关于热传导方程半离散差分格式的一个注记

本文研究了热传导方程初边值问题的半离散化差分格式直接解算法.分别从Dirichlet和Neumann边界条件出发,直接由空间差分格式导出与时间相关的一阶常微分方程组,随后通过正/余弦变换获得了原方程的半解析解,并给出了相关收敛性分析.并对中心差分格式和紧差分格式的精度差异,通过矩阵特征值理论给出了相关原因分析.另外,对于二维热传导方程初边值问题,应用矩阵张量积运算,该直接解算法可直接演变成二重正(余)弦变换.该方法由于不涉及时间上的离散,从而具有较好的计算效率.     

发展方程初边值问题的高阶差分-边界积分方程法及误差分析

本文结合差分方法与边界积分方程方法,提出并研究了一类新的求解发展型方程初边值问题的高阶差分与边界积分方程耦合数值方法.对于有界区域问题与无界区域问题给出了数值计算格式及其误差的先验估计.     

对流占优扩散方程的特征线楔形基无网格法

本文研究了一维对流占优扩散方程的初边值问题.利用特征线法与楔形基无网格法,获得了特征线楔形基无网格显格式与隐格式算法.数值实验表明算法具有精度高、计算简单等优点.     

三维变系数椭圆型方程数值求解的交替方向法

利用交替方向隐格式研究了一类三维变系数椭圆方程的边值问题,给出了交替方向法的推导过程,建立了相应的误差分析,并进行了数值模拟,结果表明,该格式具有易于计算、求解精确度高等优点.     

求解Klein-Gordon-Schrdinger方程组的一个新型守恒差分算法的收敛性分析

对复Schrdinger场和实Klein-Gordon场相互作用下一类耦合方程组的初边值问题进行了数值研究,提出了一个高效差分格式,该格式非耦合且为半显格式,因此比隐格式具有更快的计算速度,而且便于并行计算;同时,该格式很好地模拟了初边值问题的守恒性质,保证了格式计算的可靠性,从而便于长时间计算.细致讨论了格式的守恒性质,并在先验估计的基础上运用能量方法分析了差分格式的收敛性.     

Numerical verification of stationary solutions for Navier–Stokes problems

We present a numerical method to enclose stationary solutions of the Navier–Stokes equations, especially 2-D driven cavity problem with regularized boundary condition. Our method is based on the infinite dimensional Newton's method by estimating the inverse of the corresponding linearized operator. The method can be applied to the case for high Reynolds numbers and we show some numerical examples which confirm us the actual effectiveness.     

Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data

We apply the trial method for the solution of Bernoulli's free boundary problem when the Dirichlet boundary condition is imposed for the solution of the underlying Laplace equation, and the free boundary is updated according to the Neumann boundary condition. The Dirichlet boundary value problem for the Laplacian is solved by an exponentially convergent boundary element method. The update rule for the free boundary is derived from the linearization of the Neumann data around the actual free boundary. With the help of shape sensitivity analysis and Banach's fixed‐point theorem, we shed light on the convergence of the respective trial method. Especially, we derive a stabilized version of this trial method. Numerical examples validate the theoretical findings.Copyright © 2014 John Wiley & Sons, Ltd.     

Error analysis of a weighted least-squares finite element method for 2-D incompressible flows in velocity–stress–pressure formulation

In this paper we are concerned with a weighted least-squares finite element method for approximating the solution of boundary value problems for 2-D viscous incompressible flows. We consider the generalized Stokes equations with velocity boundary conditions. Introducing the auxiliary variables (stresses) of the velocity gradients and combining the divergence free condition with some compatibility conditions, we can recast the original second-order problem as a Petrovski-type first-order elliptic system (called velocity–stress–pressure formulation) in six equations and six unknowns together with Riemann–Hilbert-type boundary conditions. A weighted least-squares finite element method is proposed for solving this extended first-order problem. The finite element approximations are defined to be the minimizers of a weighted least-squares functional over the finite element subspaces of the H¹ product space. With many advantageous features, the analysis also shows that, under suitable assumptions, the method achieves optimal order of convergence both in the L²-norm and in the H¹-norm. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.     

Well-posedness of the IBVP for 2-D Euler equations with damping

In this paper we focus on the initial-boundary value problem of the 2-D isentropic Euler equations with damping. We prove the global-in-time existence of classical solution to the initial-boundary value problem for small smooth initial data by the method of local existence of solution combined with a priori energy estimates, where the appropriate boundary condition plays an important role.     

Observer design for wave equation with a forcing term in the boundary

This paper investigates the observer design problem for 1D wave equation with nonlinear boundary condition containing a forcing term, whose dynamics presents spatiotemporal chaotic behaviors. By introducing a linear error input on the left-end boundary, we construct an observer via the method of characteristics. Moreover, we present a sufficient and necessary condition for the stability of the error dynamics system. Numerical simulations are presented to illustrate the theoretical outcomes.     

The Airy equation with nonlocal conditions

We study a third-order dispersive linear evolution equation on the finite interval subject to an initial condition and inhomogeneous boundary conditions but, in place of one of the three boundary conditions that would typically be imposed, we use a nonlocal condition, which specifies a weighted integral of the solution over the spatial interval. Via adaptations of the Fokas transform method (or unified transform method), we obtain a solution representation for this problem. We also study the time periodic analog of this problem, and thereby obtain long time asymptotics for the original problem with time periodic boundary and nonlocal data.     

三维Poisson方程外问题的高阶局部人工边界条件

１引言假设Ｒ３是一分片光滑的闭曲面．是以为边界的无界区域,=Ｒ3是以为边界的有界区域,并且存在球Ｂ0＝ｘｘＲ0我们考虑下面Ｐｏｉｓｓｏｎ方程的外问题：这里f(x）,ｇ（x）是,上的已知函数,f(x)的支集是紧的,即存在一个球面=x·x=R1,使得x＝xｘＲ１,有ｆx＝０．令＝,则ｆ（ｘ）的支集包含在中,令＝xx＝,表示u在上的外法向微商．用流量为零的条件代替无限远处条件（３）,则我们得到一个新的外问题：我们将分别讨论问题（１）－（３）和（４）－（７）的数值解．由于求解区域的无界性,给数值计算带来了本质性的困难．克服此…     

Differentiability and its asymptotic analysis for nonlinear singularly perturbed boundary value problem

In this paper, we show differentiability of solutions with respect to the given boundary value data for nonlinear singularly perturbed boundary value problems and its corresponding asymptotic expansion of small parameter. This result fills the gap caused by the solvability condition in Esipova’s result so as to lay a rigorous foundation for the theory of boundary function method on which a guideline is provided as to how to apply this theory to the other forms of singularly perturbed nonlinear boundary value problems and enlarge considerably the scope of applicability and validity of the boundary function method. A third-order singularly perturbed boundary value problem arising in the theory of thin film flows is revisited to illustrate the theory of this paper. Compared to the original result, the imposed potential condition is completely removed by the boundary function method to obtain a better result. Moreover, an improper assumption on the reduced problem has been corrected.     

NUMERICAL SOLUTIONS OF PARABOLIC PROBLEMS ON UNBOUNDED 3-D SPATIAL DOMAIN

In this paper,the numerical solutions of heat equation on 3-D unbounded spatial do-main are considered. n artificial boundary Γ is introduced to finite the computationaldomain.On the artificial boundary Γ,the exact boundary condition and a series of approx-imating boundary conditions are derived,which are called artificial boundary conditions.By the exact or approximating boundary condition on the artificial boundary,the originalproblem is reduced to an initial-boundary value problem on the bounded computationaldomain,which is equivalent or approximating to the original problem.The finite differencemethod and finite element method are used to solve the reduced problems on the finitecomputational domain.The numerical results demonstrate that the method given in thispaper is effective and feasible.     

Existence of solutions to gas expansion problem through a sharp corner for 2-D Euler equations with general equation of state

In this article, we study the gas expansion problem by turning a sharp corner into a vacuum for the two-dimensional (2-D) pseudosteady compressible Euler equations with a convex equation of state. This problem can be considered as the interaction of a centered simple wave with a planar rarefaction wave. To obtain the global existence of a solution up to the vacuum boundary of the corresponding 2-D Riemann problem, we consider several Goursat-type boundary value problems for 2-D self-similar Euler equations and use the ideas of characteristic decomposition and bootstrap method. Further, we formulate 2-D-modified shallow water equations newly and solve a dam-break-type problem for them as an application of this work. Moreover, we also recover the results from the available literature for certain equations of states that provide a check that the results obtained in this article are actually correct.