拟线性抛物型方程组的一类经济差分方法

拟线性抛物型方程组的一类经济差分方法韩臻，沈隆钧，符鸿源（北京应用物理与计算数学研究所）ＡＣＬＡＳＳＯＦＥＣＯＮＯＭＩＣＡＬＤＩＦＦＥＲＥＮＣＥＭＥＴＨＯＤＳＦＯＲＱＵＡＳＩ－ＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＳＹＳＴＥＭＳ￥ＨａｎＺｈｅｎ；ＳｈｅｎＬｏ...     

ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR THE PARAMETERS OF MULTI－PARAMETER DISCRETE EXPONENTIAL FAMILY

ＡＳＹＭＰＴＯＴＩＣＡＬＬＹＯＰＴＩＭＡＬＥＭＰＩＲＩＣＡＬＢＡＹＥＳＥＳＴＩＭＡＴＩＯＮＦＯＲＴＨＥＰＡＲＡＭＥＴＥＲＳＯＦＭＵＬＴＩ－ＰＡＲＡＭＥＴＥＲＤＩＳＣＲＥＴＥＥＸＰＯＮＥＮＴＩＡＬＦＡＭＩＬＹ（杨亚宁，韦来生）￥ＹａｎｇＹａｎｉｎｇ；Ｗ...     

注化学溶液油藏模拟的特征混合元方法和分析

注化学溶液油藏模拟的特征混合元方法和分析袁益让（山东大学数学系，济南２５０１００）ＴＨＥＣＨＡＲＡＣＴＥＲＩＳＴＩＣＳ－ＭＩＸＥＤＦＩＮＩＴＥＥＬＥＭＥＮＴＭＥＴＨＯＤＡＮＤＡＮＡＬＹＳＩＳＦＯＲＴＷＯＤＩＭＥＮＳＩＯＮＡＬＣＨＥＭＩＣＡＬ－ＦＬＯＯ...     

一般广义几何规划问题的一种有效数值方法

一般广义几何规划问题的一种有效数值方法张可村，杨波艇（西安交通大学）ＡＮＥＦＦＥＣＴＩＶＥＮＵＭＥＲＩＣＡＬＭＥＴＨＯＤＦＯＲＧＥＮＥＲＡＬＳＩＧＮＯＭＩＡＬＧＥＯＭＥＴＲＩＣＰＲＯＧＲＡＭＭＩＮＧＰＲＯＢＬＥＭＳ￥ＺｈａｎｇＫｅ－ｃｕｎ；ＹａｎｇＢ...     

MAJOR－EFFICIENT SOLUTIONS AND WEAKLY MAJOR－EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING

ＭＡＪＯＲ－ＥＦＦＩＣＩＥＮＴＳＯＬＵＴＩＯＮＳＡＮＤＷＥＡＫＬＹＭＡＪＯＲ－ＥＦＦＩＣＩＥＮＴＳＯＬＵＴＩＯＮＳＯＦＭＵＬＴＩＯＢＪＥＣＴＩＶＥＰＲＯＧＲＡＭＭＩＮＧ￥ＨＵＹＵＤＡ（Ｄｅｐｔ．ｏｆＡｐｐｌ．Ｍａｔｈ．，ＳｈａｎｇｈａｉＪｉａｏＴｏｎ...     

DYNAMICAL BEHAVIORS FOR A THREE－DIMENSIONAL DIFFERENTIAL EQUATION IN CHEMICAL SYSTEM

ＤＹＮＡＭＩＣＡＬＢＥＨＡＶＩＯＲＳＦＯＲＡＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＩＮＣＨＥＭＩＣＡＬＳＹＳＴＥＭＬＩＮＹＩＰＩＮＧ（ＳｅｃｔｉｏｎｏｆＭａｔｈｅｍａｔｉｃｓ，ＫｕｎｍｉｎｇＩｎｓｔｉｔｕｔｅｏｆＴ...     

FOURIER PSEUDOSPECTRAL－FINITE DIFFERENCE METHOD FOR TWO－DIMENSIONAL VORICITY EQUATION

ＦＯＵＲＩＥＲＰＳＥＵＤＯＳＰＥＣＴＲＡＬ－ＦＩＮＩＴＥＤＩＦＦＥＲＥＮＣＥＭＥＴＨＯＤＦＯＲＴＷＯ－ＤＩＭＥＮＳＩＯＮＡＬＶＯＲＩＣＩＴＹＥＱＵＡＴＩＯＮ￥ＧＵＯＢＥＮＹＵ；ＸＩＯＮＧＹＵＥＳＨＡＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，...     

间断系数变分不等方程的无限元方法

间断系数变分不等方程的无限元方法冯慧，应隆安（北京大学数学系）ＩＮＦＩＮＩＴＥＥＬＥＭＥＮＴＭＥＴＨＯＤＦＯＲＶＡＲＩＡＴＩＯＮＡＬＩＮＥＱＵＡＬＩＴＩＥＳＷＩＴＨＤＩＳＣＯＮＴＩＮＵＯＵＳＣＯＥＦＦＩＣＩＥＮＴＳ￥ＦｅｎｇＨｕｔ；ＹｉｎｇＬｏｎｇ－...     

A MODEL FOR WHITE NOISE ANALYSIS IN P-ADIC NUMBER FIELDS

ＡＭＯＤＥＬＦＯＲＷＨＩＴＥＮＯＩＳＥＡＮＡＬＹＳＩＳＩＮＰ－ＡＤＩＣＮＵＭＢＥＲＦＩＥＬＤＳ（黄志远）￥ＡｎｄｒｅｗＫｈｒｅｎｎｉｋｏｖ（ＭｏｓｃｏｗＩｎｓｔ．ｏｆＥｌｅｃｔｒｏｎｉｃＥｎｇｉｎｅｅｒｉｎｇ，１０３４９８，Ｚｅｌｅｎｏｇｒａｄ，Ｋ－...     

THE ERRORS ESTIMATION OF THE CHEBYSHEV SPECTRAL－DIFFERENCE METHOD FOR TWO－DIMENSIONAL VORTICITY EQUATION

ＴＨＥ　ＥＲＲＯＲＳ　ＥＳＴＩＭＡＴＩＯＮ　ＯＦ　ＴＨＥ　ＣＨＥＢＹＳＨＥＶ　ＳＰＥＣＴＲＡＬ－ＤＩＦＦＥＲＥＮＣＥ　ＭＥＴＨＯＤ　ＦＯＲ　ＴＷＯ－ＤＩＭＥＮＳＩＯＮＡＬ　ＶＯＲＴＩＣＩＴＹ　ＥＱＵＡＴＩＯＮＴＨＥＥＲＲＯＲＳＥＳＴＩＭＡＴＩＯＮＯＦ...     

Implicit kinetic schemes for scalar conservation laws

Based on kinetic formulation for scalar conservation laws, we present implicit kinetic schemes. For time stepping these schemes require resolution of linear systems of algebraic equations. The scheme is conservative at steady states. We prove that if time marching procedure converges to some steady state solution, then the implicit kinetic scheme converges to some entropy steady state solution. We give sufficient condition of the convergence of time marching procedure. For scalar conservation laws with a stiff source term we construct a stiff numerical scheme with discontinuous artificial viscosity coefficients that ensure the scheme to be equilibrium conserving. We couple the developed implicit approach with the stiff space discretization, thus providing improved stability and equilibrium conservation property in the resulting scheme. Numerical results demonstrate high computational capabilities (stability for large CFL numbers, fast convergence, accuracy) of the developed implicit approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 26–43, 2002     

Numerical viscosity and the entropy condition

Weak solutions of hyperbolic conservation laws are not uniquely determined by their initial values; an entropy condition is needed to pick out the physically relevant solutions. The question arises whether finite difference approximations converge to this particular solution. It is known that this is not always the case with the standard Lax-Wendroff (L-W) difference scheme. In this paper a simple variant of the L-W scheme is devised which retains its desirable computational features—conservation form, three point scheme, second-order accuracy on smooth solutions, but which has the additional property that limit solutions satisfy the entropy condition. This variant is constructed by adding a simple nonlinear artificial viscosity to the usual L-W operator. The nature of the viscosity is deduced by first analyzing a model differential equation derived from the truncation error for the L-W operator, keeping only terms of order (Δx)². Furthermore, this viscosity is “switched on” only when sufficiently steep discrete gradients develop in the approximate solution: The full L-W scheme is then shown to have the desired property provided that the Courant-Friedrichs-Lewy restriction |λf′(u)|≤0.14 is satisfied.     

FINITE DIFFERENCE APPROXIMATION FOR PRICING THE AMERICAN LOOKBACK OPTION

In this paper we are concerned with the pricing of lookback options with American type constrains. Based on the differential linear complementary formula associated with the pricing problem, an implicit difference scheme is constructed and analyzed. We show that there exists a unique difference solution which is unconditionally stable. Using the notion of viscosity solutions, we also prove that the finite difference solution converges uniformly to the viscosity solution of the continuous problem. Furthermore, by means of the variational inequality analysis method, the O（△t ＋ △x^2）-order error estimate is derived in the discrete L2-norm provided that the continuous problem is sufficiently regular. In addition, a numerical example is provided to illustrate the theoretical results.     

A numerical method for pricing European options with proportional transaction costs

In the paper, we propose a numerical technique based on a finite difference scheme in space and an implicit time-stepping scheme for solving the Hamilton–Jacobi–Bellman (HJB) equation arising from the penalty formulation of the valuation of European options with proportional transaction costs. We show that the approximate solution from the numerical scheme converges to the viscosity solution of the HJB equation as the mesh sizes in space and time approach zero. We also propose an iterative scheme for solving the nonlinear algebraic system arising from the discretization and establish a convergence theory for the iterative scheme. Numerical experiments are presented to demonstrate the robustness and accuracy of the method.     

Numerical analysis for a locally damped wave equation

We consider a semi-discrete finite element formulation with artificial viscosity for the numerical approximation of a problem that models the damped vibrations of a string with fixed ends. The damping coefficient depends on the spatial variable and is effective only in a sub-interval of the domain. For this scheme, the energy of semi-discrete solutions decays exponentially and uniformly with respect to the mesh parameter to zero. We also introduce an implicit in time discretization. Error estimates for the semi-discrete and fully discrete schemes in the energy norm are provided and numerical experiments performed.     

Analytical solutions to detect the scheme dispersion for the coupled nonlinear equations

It is shown, how even particular traveling wave asymptotic solution may describe the defects on the shock wave profile caused by the dispersion features of the numerical scheme of the coupled nonlinear gas dynamics equations. For this purpose the coupled nonlinear partial differential equations or the so-called differential approximation of the scheme, are obtained, and a simplification of the method of differential approximation is suggested to obtain the desired asymptotic solution. The solution is used to study the roles of artificial viscosity and the refinement of the mesh for the suppression of the dispersion of the scheme.     

Grid solution of problem with unilateral constraints

The present study deals with the solution of a problem, defined in a three-dimensional domain, arising in fluid mechanics. Such problem is modelled with unilateral constraints on the boundary. Then, the problem to solve consists in minimizing a functional in a closed convex set. The characterization of the solution leads to solve a time-dependent variational inequality. An implicit scheme is used for the discretization of the time-dependent part of the operator and so we have to solve a sequence of stationary elliptic problems. For the solution of each stationary problem, an equivalent form of a minimization problem is formulated as the solution of a multivalued equation, obtained by the perturbation of the previous stationary elliptic operator by a diagonal monotone maximal multivalued operator. The spatial discretization of such problem by appropriate scheme leads to the solution of large scale algebraic systems. According to the size of these systems, parallel iterative asynchronous and synchronous methods are carried out on distributed architectures; in the present study, methods without and with overlapping like Schwarz alternating methods are considered. The convergence of the parallel iterative algorithms is analysed by contraction approaches. Finally, the parallel experiments are presented.     

Newton iterations in implicit time-stepping scheme for differential linear complementarity systems

We propose a generalized Newton method for solving the system of nonlinear equations with linear complementarity constraints in the implicit or semi-implicit time-stepping scheme for differential linear complementarity systems (DLCS). We choose a specific solution from the solution set of the linear complementarity constraints to define a locally Lipschitz continuous right-hand-side function in the differential equation. Moreover, we present a simple formula to compute an element in the Clarke generalized Jacobian of the solution function. We show that the implicit or semi-implicit time-stepping scheme using the generalized Newton method can be applied to a class of DLCS including the nondegenerate matrix DLCS and hidden Z-matrix DLCS, and has a superlinear convergence rate. To illustrate our approach, we show that choosing the least-element solution from the solution set of the Z-matrix linear complementarity constraints can define a Lipschitz continuous right-hand-side function with a computable Lipschitz constant. The Lipschitz constant helps us to choose the step size of the time-stepping scheme and guarantee the convergence.     

带对流项的渗流型方程的显格式

１．引言　假设有一种不可压流体在一均匀的、各向同性的刚性多孔柱形介质中流动,流动沿着与水平方向成ａ角进行,则可用下述方程描述其中λ＝ｓｉｎα,ｕ表示介质的含湿度．λ＝０,即表示沿水平方向流动,它和λ≠０的情形分别称为无对流项和有对流项的渗流方程．它们可分别写成下面一般的形式：　渗流型方程是退化抛物型方程,由于它可有退化点（使二阶导数项系数为零的点）,它与正规抛物型方程有很大区别．正规抛物型方程有充分光滑的古典解,渗流方程则不然．即使初值充分光滑,也不能保证渗流方程有光滑的解．实际上,渗流方程可有…     

Semi‐implicit schemes for transient Navier–Stokes equations and eddy viscosity models

This study presents two computational schemes for the numerical approximation of solutions to eddy viscosity models as well as transient Navier–Stokes equations. The eddy viscosity model is one example of a class of Large Eddy Simulation models, which are used to simulate turbulent flow. The first approximation scheme is a first order single step method that treats the nonlinear term using a semi‐implicit discretization. The second scheme employs a two step approach that applies a Crank–Nicolson method for the nonlinear term while also retaining the semi‐implicit treatment used in the first scheme. A finite element approximation is used in the spatial discretization of the partial differential equations. The convergence analysis for both schemes is discussed in detail, and numerical results are given for two test problems one of which is the two dimensional flow around a cylinder. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009