UNIFORM DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED LINEAR 2ND ORDER HYPERBOLIC PROBLEM WITH ZEROTH ORDER REDUCED EQUATION

In this paper a singularly perturbed linear second order hyperbolic problem with zerothorder reduced equation is discussed.Firstly,an energy inequality of the solution and anestimate of the remainder term of the asymptotic solution are given.Then an exponentiallyfitted difference scheme is developed in an equidistant mesh.Finally,uniform convergencein small parameter is proved in the sense of discrete energy norm.     

A UNIFORMLY CONVERGENT DIFFERENCE SCHEME FOR THE SINGULAR PERTURBATION PROBLEM OF A HIGH ORDER ELLIPTIC DIFFERENTIAL EQUATION

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NUMERICAL SOLUTION OF QUASILINEAR SINGULARLY PERTURBED ORDINARY DIFFERENTIAL EQUATION WITHOUT TURNING POINTS

In this paper we consider a quasilinear second order ordinary differential equation equation witha small parameter e.Firstly an approximate problem is constructed.Then an iterativeprocedure is developed.Finally we give an algorithm whose accuracy is good for arbitraryε>0.     

APPLICATIONS OF THE EXTRAPOLATION METHOD TO THE NUMERICAL SOLUTION OF SINGULAR PERTURBATION PROBLEMS

In this paper we consider applications of extrapolation method to the numericalsolution of singular perturbation problem for elliptic—parabolic equation in order tomanifesting accuracy of approximations and estimate the order of accuracy,Concerningthe uniform convergence in ref.[1].its proof is given in the appendix.     

具有非光滑边界层函数的线性变系数抛物型方程初边值问题的差分格式

本文利用非均匀网格和指数型拟合差分方法给出了具有非光滑边界层函数的线性抛物型方程关于小参数ε一致收敛的差分格式.文章还给出了误差估计和数值结果.     

双曲-双曲奇异摄动问题的指数型拟合差分格式

本文讨论带有关于x的一阶导数项的双曲奇异摄动初边值问题,在较弱的相容性条件下构造了问题的渐近解并证明了解的一致有效性.然后我们对原问题构造一个指数型拟合差分格式并建立了离散能量不等式.最后我们证明差分问题的解一致收敛于原问题的精确解.     

NUMERICAL SOLUTION OF THE SINGULARLY PERTURBED PROBLEM FOR THE HYPERBOLIC EQUATION WITH INITIAL JUMP

In this paper we consider the initial-boundary value problem for a second orderhyperbolic equation with initial jump.The bounds on the derivatives of the exact solutionare given.Then a difference scheme is constructed on a non-uniform grid.Finally,uniformconvergence of the difference solution is proved in the sense of the discrete energy norm.     

Uniform difference scheme for a singularly perturbed linear 2nd order hyperbolic problem with zeroth order reduced equation

In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.     

Difference scheme for an initial-boundary value problem for linear coefficient-varied parabolic differential equation with a nonsmooth boundary layer function

In this paper, using nonumiform mesh and exponentially fitted difference method,a uniformly convergent difference scheme .for an initial-boundary value problem of linear parabolic differential equation with the nonsmooth boundary layer function with respect to small parameter ε is given, and error estimate and numerical result are also given.