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无共振转向点问题的数值解

林鹏程 颜鹏翔

林鹏程, 颜鹏翔. 无共振转向点问题的数值解[J]. 应用数学和力学, 1985, 6(5): 423-430.
引用本文: 林鹏程, 颜鹏翔. 无共振转向点问题的数值解[J]. 应用数学和力学, 1985, 6(5): 423-430.
Lin Peng-cheng, Yan Peng-xiang. The Numerical Solution for Problems of Turning Point Without Resonance[J]. Applied Mathematics and Mechanics, 1985, 6(5): 423-430.
Citation: Lin Peng-cheng, Yan Peng-xiang. The Numerical Solution for Problems of Turning Point Without Resonance[J]. Applied Mathematics and Mechanics, 1985, 6(5): 423-430.

无共振转向点问题的数值解

The Numerical Solution for Problems of Turning Point Without Resonance

  • 摘要: 本文用Kellogg[3]的估计方法,证明了IL'in[1]格式对于无共振转向点问题具有一阶的一致收敛性,并证明了这个估计是最佳的.
  • [1] IL in,A.M,Differencing scheme for a differential equation with a small parameter affecting the highest derivative,Mat.Zametiki.,6(1969),237-248.
    [2] 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.
    [3] Kellogg,R.B.,Difference Approximation for a Singular Perturbation Problem with Turuing 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.
    [4] Jiang Fu-ru.,On boundary value problems for a class of ordinary differential equations with turning points,App.Math.Mech.,1.2(1980),201-213.
    [5] 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,Ireland(1980).
    [6] Ackerberg,R.C.and R.E.O'Malley,Boundary Layer problem exhibiting resonance,Studies in Appl.Math.,49,3(1970),277-295.
    [7] 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.,14-18,(1982).
    [8] Lakin,W.D.,Boundary value problems with a turning point,Studies in Appl.Math,51,3(1972),261-275.
    [9] O'Malley,R.E.,Introduction to Singular Perturbations,Acad.Press,New York and London(1974).
    [10] Cook,L.P.and W.Eckhaus,Resonance in a boundary value problem of singular perturbation type,Studies in Appl.Math.,52,2(1973),129-139.
    [11] Varga,R S.,Matrix Iterative Analysis,Prentice-Hall,Englewood Cliffs,N.J.,USA(1962).
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出版历程
  • 收稿日期:  1984-03-21
  • 刊出日期:  1985-05-15

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