留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

解含转向点问题的完全指数型拟合差分方法

陈明伦 王国英

陈明伦, 王国英. 解含转向点问题的完全指数型拟合差分方法[J]. 应用数学和力学, 1990, 11(1): 67-77.
引用本文: 陈明伦, 王国英. 解含转向点问题的完全指数型拟合差分方法[J]. 应用数学和力学, 1990, 11(1): 67-77.
Chen Ming-lun, Wang Guo-ying. Completely Exponentially Fitted Finite Difference Methods for Problems of Turning Point[J]. Applied Mathematics and Mechanics, 1990, 11(1): 67-77.
Citation: Chen Ming-lun, Wang Guo-ying. Completely Exponentially Fitted Finite Difference Methods for Problems of Turning Point[J]. Applied Mathematics and Mechanics, 1990, 11(1): 67-77.

解含转向点问题的完全指数型拟合差分方法

Completely Exponentially Fitted Finite Difference Methods for Problems of Turning Point

  • 摘要: 本文对含转向点的微分方程边值问题建立了完全指数型拟合差分格式,证明了此格式具有一阶一致收敛性.推广了Miller[1]的方法,简化了证明过程.数值结果表明本格式比Il'in[2]格式要好.
  • [1] Carroll,J.and J.J.H.Miller,Completely exponentially fitted finite difference schemes for some singular perturbation problems,boundary and interior layers,Computational and Asymptotic Methods,Ed.J.J.H.Miller,Boole Press,Dublin(1980),225-230.
    [2] Il'in,A.M.,Differencing scheme for a differetial equation with a small parameter affecting the highest derivative,Math.Notes Acad.Sci.,USSR.6(1969),596-602.
    [3] Miller,J.J.H.,Sufficient conditions for the convergence uniformly in ε,of a three-point difference scheme for a singular perturbation problem,Proc.Oberwolfach,Germany,Lecture Notes in Maths.,Springer-Verlag,679(1977),85-91.
    [4] Kellogg,R.B.,Difference approximation for a singular perturbation problem with turning points,Analysis and numerical approaches to asymptotic problems in analysis,S.Axelsson,L.S.Frank,V.Slusis(eds),North-Holland Publishing Company(1981),133-139.
    [5] Farrell,P.A.,A uniformly convergent difference scheme for turning point problems,The First Conference on Boundary and Interior Layers-Computation and Asymptotic Methods,Dublin,Ireland,Jan.(1982),14-18.
    [6] 林鹏程、颜鹏翔,无共振转向点问题的数值解,应用数学和力学,6, 5 (1985), 403-430.
    [7] Ackerberg,R.C.and R.E.O'Malley,Boundary layer problem exhibiting resonance,Studies in Appl.Math.,49,3(1970).277-295.
    [8] Lakin,W.D.,Foundary value problems with a turning point,Studies in Appl.Math.,51,3(1972),261-275.
    [9] O'Malley,R.E.,Introdution Singular Perturbations,Acad.Press,New York and London(1974).
    [10] Cook,L.P.and W.Eckhaus,Resonance in boundary value problem of singular perturbation type,Studies in Appl.Math.,52,2(1973),129-139.
    [11] Doolan,E.P.,J.J.H.Miller and W.H.A.Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Layers,Boole Press,Dublin,(1980).
    [12] Kellogg,R.B.and A.Tsan,Analysis of some difference approximations for a singular perturbation problem without turning point,Math.Comp.,32(1978),1025-1039.
    [13] Jiang Fu-ru,On the boundary value problems for a class of ordinary differential equations with turning points,Appl.Math and Mech.,1,2(1980),201-213.
  • 加载中
计量
  • 文章访问数:  1717
  • HTML全文浏览量:  80
  • PDF下载量:  525
  • 被引次数: 0
出版历程
  • 收稿日期:  1988-05-05
  • 刊出日期:  1990-01-15

目录

    /

    返回文章
    返回