A NUMERICAL EMBEDDING METHOD FOR SOLVING THE NONLINEAR COMPLEMENTARITY PROBLEM(Ⅱ)-ALGORITHM AND ITS CONVERGENCE

In this paper,based on the results presented in part Ⅰ of this paper[18],we present a numerical embedding algorithm for solving the nonlinear complementarityproblem, and prove its convergence carefully. Numerical experiments show that thealgorithm is successful.     

A NUMERICAL EMBEDDING METHOD FOR SOLVING THE NONLINEAR COMPLEMENTARITY PROBLEM（II）-ALGORITHM AND ITS CONVERGENCE

In this paper, based on the results presented in part I of this paper[18],we present a numerical embedding algorithm for solving the nonlinear complementarityproblem, and prove its convergence carefully. Numerical experiments show that thealgorithm is successful.     

A NEW SQP-FILTER METHOD PROGRAMMING FOR SOLVING NONLINEAR PROBLEMS

In [4], Fletcher and Leyffer present a new method that solves nonlinear programming problems without a penalty function by SQP-Filter algorithm. It has attracted much attention due to its good numerical results. In this paper we propose a new SQP-Filter method which can overcome Maratos effect more effectively. We give stricter acceptant criteria when the iterative points are far from the optimal points and looser ones vice-versa. About this new method, the proof of global convergence is also presented under standard assumptions. Numerical results show that our method is efficient.     

INEXACT DAMPED NEWTON METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS

In this paper, we propose an inexact clamped Newton method for solving nonlinear complementarity problems based on the equivalent B-differentiable equations.Global convergence and locally quadratic convergence are obtained,and numerical results are given.     

A NEW NUMERICAL METHOD FOR TWO-PHASE IMMISCIBLE INCOMPRESSIBLE PROBLEM

Two-phase, immiscible, incompressible flow in porous media is governed by a system of nonlinear partial differential equations. In most practical applications convection physically dominates diffusion, and the object of this paper is to develop a finite difference method combined with the method of characteristics and the lumped mass method to treat the parabolic equation of the differential system. This method is shown satisfy the maximum principle and its error analysis is presented.     

A BRANCH-AND-PRICE ALGORITHM FOR SOLVING THE CUTTING STRIPS PROBLEM

After giving a suitable model for the cutting strips problem, we present a branch-and-price algorithm for it by combining the column generation technique and the branch-and-hound method with LP relaxations. Some theoretical issues and implementation details about the algorithm are discussed, including the solution of the pricing subproblem, the quality of LP relaxations, the branching scheme as well as the column management. Finally, preliminary computarional experience is reported.     

A CONTOUR INTEGRATION METHOD FOR SOLVING THE FADDEEV EQUATION

We have found a contour for integration of Faddeev equation which is differ ent from the contour given by Cahill and Sloan. The essential point of our method is that a better mathematical expression of the kernel function for the Faddeev equation is given. With this expression, the values of the function in the neighbourhood of the origin can be calculated, whatever the values of l are. In the work of Cahill and Slcan only l=0, 1, 2, 3 can be rigorously calculated, but in this paper, we can calculate forl=0, 1, 2, ……, 8 rigorously.     

A DIRECT METHOD FOR THE UNIT CIRCLE PROBLEM

The unit circle problem is the problem of finding the number of eigenvalues of a non-Hermitian matrix inside and outside the unit circle . To reduce the cost of computing eigenvalues for the problem, a direct method, which is analogous to that given in [5], is proposed in this paper.     

A CONTOUR INTEGRATION METHOD FOR SOLVING THE FADDEEV EQUATION

We have found a contour for integration of Faddeev equation which is differ ent from the contour given by Cahill and Sloan. The essential point of our method is that a better mathematical expression of the kernel function for the Faddeev equation is given. With this expression, the values of the function in the neighbourhood of the origin can be calculated, whatever the values of ι are. In the work of Cahill and Slcan only ι=0, 1, 2, 3 can be rigorously calculated, but in this paper, we can calculate for ι=0, 1、2,……, 8 rigorously.     

A NONLOCAL NONLINEAR BOUNDARYVALUE PROBLEM FOR THE HEAT EQUATIONS

51.IntroductionandMalnResultsLetflCR"(n=2or3)beaboundedsmoothdomainwithboundaryan=r1ur2,wherer1nr2=Oandr1,r2/O.Weconsiderthefollowingmixedinitial-boundaryvalueproblemfortheheatequation'whereH'DHCR-Risastrict1ydecreasingtunction,ustancnormalvectorattheboundary.Theboundaryconditiononr2appearsinthermistors.Howison,RodriguesandShillorl1]studiedsuchkindofboundaryvalueproblemforellipticequations.HerewesupposethatHisonto'nH=R,andwherea,bdenote,andwillalwaysdenote,varieskindofconstants.Underhy…     

A CONTROL PROBLEM FOR REACTOR THEORY

In this paper we are concerned with a control problem for a reactor whose dynamics is governed by the diffusion approximate equation. With the variance index, we show the existence and the uniqueness of optimal controllable macro-absorption cross section and give the corresponding optimality conditions.     

AN ITERATIVE METHOD FOR THE MINIMAX PROBLEM

In this paper a class of iterative methods for the minimax problem i; proposed.We present a sequence of the extented linear-quadratic programming (ELQP) problems as subproblems of the original minimal problem and solve the ELQP problem iteratively.The locally linear and su-perlinear convergence results of the algorithm are established.     

AN ITERATIVE METHOD FOR SOLVING THE SINGULAR POINTS

An iterative method for solving a 2-order singular point is proposed in this paper. This method possesses the advantages of very fast convergent rate and higher accuracy.     

A COLLOCATION METHOD FOR THE CONDUCTIVITY PROBLEM WITH DISCONTINUOUS COEFFICIENT

In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the 7 is a piecewise constant function. By the integral representation formula of the solution of the conductivity equation on the boundary and interface, the boundary integral equations are obtained. We discuss the properties of these integral equations and propose a collocation method for solving these boundary integral equations. Both the theoretical analysis and the error analysis are presented and a numerical example is given.     

A UNIFORM NUMERICAL METHOD FOR QUASILINEAR SINGULAR PERTURBATION PROBLEM WITH A TURNING POINT

A nonlinear difference scheme is given for solving a quasilinear siagularly perturbed two-point boundary value problem with a turning point. The method uses non-equidistant discretization meshes. The solution of the scheme is shown to be first order accurate in the discrete L^∞ norm, uniformly in the perturbation parameter.     

A NUMERICAL PERTURBATION EXPANSION METHOD FOR THE SOLUTION OF A LIENARD-TYPE INITIAL-VALUE PROBLEM WITH PERIODIC DECAYING FORCING TERM

A numerical perturbation expansion method is developed, analysed and implemented for the numerical solution of a second-order initial-value problem. The differential equation in this problem exhibits cubic damping, a cubic restoring force and a decaying forcing-term which is periodic with constant frequency. The method is compared with the numerical method by Twizell [1]. In fact, the later is first perturbation approximate solution in the present paper.     

A REGULARIZATION NEWTON METHOD FOR MIXED COMPLEMENTARITY PROBLEMS

In this paper, a regularization Newton method for mixed complementarity problem(MCP) based on the reformulation of MCP in [1] is proposed. Its global conver-gence is proved under the assumption that F is a Po-function. The main feature of our algorithm is that a priori of the existence of an accumulation point for convergence need not to be assumed.     

A QUASI-NEWTON METHOD IN INFINITE-DIMENSIONAL SPACES AND ITS APPLICATION FOR SOLVING A PARABOLIC INVERSE PROBLEM

1.IntroductionQuasi-Newtonmethodsplayanimportantroleinnumericallysolvingnon--linearsystemsofequationsontheEuclideanspaces.Blltitseemsthatthequasi-Newtonmethodshavenotbeenapplieddirectlytosolvinginverseproblemsinpartialdifferentialequations(PDE)uptonowifwe…     

THE CAUCHY PROBLEM FOR A CLASS OF DOUBLY DEGENERATE NONLINEAR PARABOLIC EQUATION

This article studies the Cauchy problem for a class of doubly nonlinear degenerate parabolic equations . Under certain conditions, the author considers its regularized problem and establishes some estimates. On the basis of the estimates, the existence and uniqueness of the generalized solutions in BV space are proved.     

A FINITE DIFFERENCE SCHEME FOR SOLVING THE NONLINEAR POISSON-BOLTZMANN EQUATION MODELING CHARGED SPHERES

In this work, we propose an efficient numerical method for computing the electrostaticinteraction between two like-charged spherical particles which is governed by the nonlinearPoisson-Boltzmann equation. The nonlinear problem is solved by a monotone iterativemethod which leads to a sequence of linearized equations. A modified central finite differ-ence scheme is developed to solve the linearized equations on an exterior irregular domainusing a uniform Cartesian grid. With uniform grids, the method is simple, and as aconsequence, multigrid solvers can be employed to speed up the convergence. Numericalexperiments on cases with two isolated spheres and two spheres confined in a chargedcylindrical pore are carried out using the proposed method. Our numerical schemes arefound efficient and the numerical results are found in good agreement with the previouspublished results.