LARGE－TIME BEHMIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGHPOROUS MEDIA

ＬＡＲＧＥ－ＴＩＭＥＢＥＨＭＩＯＲＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＣＯＭＰＲＥＳＳＩＢＬＥＡＤＩＡＢＡＴＩＣＦＬＯＷＴＨＲＯＵＧＨＰＯＲＯＵＳＭＥＤＩＡ￥ＸＩＡＯＬＩＮＧ（Ｌ．ＨＳＩＡＯ）Ｄ．ＳＥＲＲＥ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔ...     

一类抛物－椭圆耦合方程组混合初边值问题的二阶收敛差分格式Ⅰ

一类抛物－椭圆耦合方程组混合初边值问题的二阶收敛差分格式Ⅰ孙志忠（东南大学数学力学系）ＡＳＥＣＯＮＤ－ＯＲＤＥＲＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＦＯＲＴＨＥＭＩＸＥＤＩＮＩＴＩＡＬ－ＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＯＦＡＣＬＡＳＳＯＦＰＡＲＡ...     

一类抛物－椭圆耦合方程组混合初边值问题的二阶收敛差分格式Ⅰ

一类抛物－椭圆耦合方程组混合初边值问题的二阶收敛差分格式Ⅰ孙志忠（东南大学数学力学系）ＡＳＥＣＯＮＤ－ＯＲＤＥＲＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＦＯＲＴＨＥＭＩＸＥＤＩＮＩＴＩＡＬ－ＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＯＦＡＣＬＡＳＳＯＦＰＡＲＡ...     

WORD PROBLEMS AND THE CENTERS OF ABEL DIFFERENTIAL EQUATIONS

ＷＯＲＤ　ＰＲＯＢＬＥＭＳ　ＡＮＤ　ＴＨＥ　ＣＥＮＴＥＲＳ　ＯＦ　ＡＢＥＬ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳＷＯＲＤＰＲＯＢＬＥＭＳＡＮＤＴＨＥＣＥＮＴＥＲＳＯＦＡＢＥＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥Ｍ．Ａ．Ｍ．Ａｌｗａｓｈ...     

CAUCHY PROBLEM FOR SEMILINEAR HYPERBOLIC EQUATION OF HIGHER ORDER WITH DISCONTINUOUS INITIAL DATA

ＣＡＵＣＨＹＰＲＯＢＬＥＭＦＯＲＳＥＭＩＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＥＱＵＡＴＩＯＮＯＦＨＩＧＨＥＲＯＲＤＥＲＷＩＴＨＤＩＳＣＯＮＴＩＮＵＯＵＳＩＮＩＴＩＡＬ　ＤＡＴＡＣｈｅｎＳｈｕｘｉｎｇ（陈恕行）（Ｉｎｓｔ．ｏｆＭａｔｈ．，ＦｕｄａｎＵｎｉｖ...     

FORCED OSCILLATIONS OF HYPERBOLIC DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

ＦＯＲＣＥＤＯＳＣＩＬＬＡＴＩＯＮＳＯＦＨＹＰＥＲＢＯＬＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＤＥＶＩＡＴＩＮＧＡＲＧＵＭＥＮＴＳＣＵＩＢＡＯＴＯＮＧ（崔宝同）（ＢｉｎｚｈｏｕＮｏｒｍａｌＣｏｌｌｅｇｅ，Ｂｉｎｚｈｏｕ２５６６０４，Ｃ...     

BOUNDARY VALUE PROBLEMS FOR SECOND ORDER SELFADJOINTFUNCTIONAL DIFFERENTIAL EQUATION

ＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＳＥＣＯＮＤＯＲＤＥＲＳＥＬＦＡＤＪＯＩＮＴＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮ￥ＷｅｎｇＰｅｉｘｕａｎ（翁佩萱）（ＳｏｕｔｈＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，华南师范...     

ADMISSIBILITY OF LINEAR ESTIMATE OF REGRESSION COEFFICIENTS IN GROWTH CURVE MODEL UNDER MATRIX LOSS

ＡＤＭＩＳＳＩＢＩＬＩＴＹＯＦＬＩＮＥＡＲＥＳＴＩＭＡＴＥＯＦＲＥＧＲＥＳＳＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳＩＮＧＲＯＷＴＨＣＵＲＶＥＭＯＤＥＬＵＮＤＥＲＭＡＴＲＩＸＬＯＳＳＷＡＮＧＸＵＥＲＥＮ（王学仁）（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，...     

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

ＢＯＵＮＤＡＲＹＶＸＬＵＥＰＲＯＢＬＥＭＳＦＯＲＳＹＳＴＥＭＳＯＦＮＯＮＬＩＮＥＡＲＳＥＣＯＮＤＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＤＦＦＥＲＥＮＣＥＥＱＵＡＴＩＯＮＳ￥ＭＩＡＯＳＨＵＭＥＩＡｂｓｔｒａｃｔ：Ｔｈｅａｕｔｈｏｒｓｔｕｄｉｅｓｔｈｅｂｏｕ...     

A CLASS OF SINGULAR PERTURBATIONS FOR SECOND ORDER QUASI－LINEAR BOUNDARY VALUE PROBLEMS ON INFINITE INTERVAL

ＡＣＬＡＳＳＯＦＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＳＦＯＲＳＥＣＯＮＤＯＲＤＥＲＱＵＡＳＩ－ＬＩＮＥＡＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＮＩＮＦＩＮＩＴＥＩＮＴＥＲＶＡＬＺＨＡＯＷＥＩＬＩ（赵为礼）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈ...     

Long- time Convergence of Numerical Approximations for Semilinear Parabolic Equations(Ⅰ )

§ 0 .Introduction　 We consider the numerical approximations of the dynamical systems governed bysemilinear parabolic equations,which are discretized by Galerkin and nonlinear Galerkinmethods in space,and by Runge-Kutta method in time.The numerical approximationson a finite time interval have already been widely studied(see[1 ]— [5] ) .We areconcerned with the long-time convergence and error estimates.This article is composedof three parts. In part ,we provide an abstract framework. In§…     

Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.     

一类非定常对流占优扩散问题差分-流线扩散法的后处理

讨论了一类非定常对流占优扩散方程的差分-流线扩散格式(FDSD),利用插值后处理技术,提高了特殊网格下该FDSD格式在双线性元空间的精度,从而按L∞(L2(Ω) 模达到最优．     

非定常对流扩散问题差分-流线扩散法的线性三角元解的最优误差估计

讨论了差分-流线扩散法(FDSD)求解线性对流占优扩散问题解的精度,利用插值后处理技术,使该格式解的空间精间达到最优.     

Pointwise error estimates for a streamline diffusion finite element scheme

Summary Pointwise error estimates for a streamline diffusion scheme for solving a model convection-dominated singularly perturbed convection-diffusion problem are given. These estimates improve pointwise error estimates obtained by Johnson et al.[5].     

A posteriori error estimates for the generalized Schwarz method of a new class of advection‐diffusion equation with mixed boundary condition

In this paper, a posteriori error estimates for the generalized Schwarz method with mixed boundary condition on the interfaces for advection‐diffusion equation with second‐order boundary value problems are proved using theta time scheme combined with Galerkin spatial method. Furthermore, a asymptotic behavior in Sobolev norm is deduced using Benssoussan‐Lions' algorithm.     

EXPLICITLY SOLVABLE CHARACTERISTIC METHOD FOR CONVECTION DIFFUSION PROBLEMS

In this paper, a new method for numerically solving nonlinear convection-dominated diffusion problems is devised and analysed. The discrete time approximations with time stepping along charactcristics are cstablished and solved in spaces posscssing reproducing kernel functions. At each time step, the exact solution of the approximate problem is given by explicit expression. The computational advantage of this method is that the schemes are absolutely stable, and are explicitly solvable as well. The stability and error estimates are derived. Some numerical results are given.     

Analysis of a decoupled time‐stepping algorithm for reduced MHD system modeling magneto‐convection

In this article, we analyze the stability and error estimate of a decoupled algorithm for a magneto‐convection problem. Magneto‐convection is assumed to be modeled by a coupled system of reduced magneto‐hydrodynamic (RMHD) equations and convection‐diffusion equation. The proposed algorithm applies the second‐order backward difference formula in time and finite element in space. To obtain a noniterative decouple algorithm from the fully discrete nonlinear system, we use a second‐order extrapolation in time to the nonlinear terms such that their skew symmetry properties are preserved. We prove the stability of the algorithm and derive error estimates without assuming any stability conditions. The algorithm is unconditionally stable and requires the solution of one RMHD problem and one convection‐diffusion equation per time step. Numerical test is presented that illustrates the accuracy and efficiency of the algorithm.     

Second-order characteristic schemes in time and age for a nonlinear age-structured population model

In this paper, we analyze two new second-order characteristic schemes in time and age for an age-structured population model with nonlinear diffusion and reaction. By using the characteristic difference to approximate the transport term and the average along the characteristics to treat the nonlinear spatial diffusion and reaction terms, an implicit second-order characteristic scheme is proposed. To compute the nonlinear approximation system, an explicit second-order characteristic scheme in time and age is further proposed by using the extrapolation technique. The global existence and uniqueness of the solution of the nonlinear approximation scheme are established by using the theory of variation methods, Schauder’s fixed point theorem, and the technique of prior estimates. The optimal error estimates of second order in time and age are strictly proved for both the implicit and the explicit characteristic schemes. Numerical examples are given to illustrate the performance of the methods.     

A posteriori error estimate for finite volume approximations to singularly perturbed nonlinear convection-diffusion equations

Summary. This paper is devoted to the study of a posteriori and a priori error estimates for the scalar nonlinear convection diffusion equation . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the -norm in the situation, where the diffusion parameter is smaller or comparable to the mesh size. Numerical experiments underline the theoretical results. Received February 25, 1999 / Revised version received July 6, 1999 / Published online August 2, 2000