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二阶拟线性奇摄动常微分方程的数值解法

林平 苏煜城

林平, 苏煜城. 二阶拟线性奇摄动常微分方程的数值解法[J]. 应用数学和力学, 1989, 10(11): 955-959.
引用本文: 林平, 苏煜城. 二阶拟线性奇摄动常微分方程的数值解法[J]. 应用数学和力学, 1989, 10(11): 955-959.
Lin Ping, Su Yu-cheng. Numerical Solution of Quasilinear Singularly Perturbed Ordinary Differential Equation without Turning Points[J]. Applied Mathematics and Mechanics, 1989, 10(11): 955-959.
Citation: Lin Ping, Su Yu-cheng. Numerical Solution of Quasilinear Singularly Perturbed Ordinary Differential Equation without Turning Points[J]. Applied Mathematics and Mechanics, 1989, 10(11): 955-959.

二阶拟线性奇摄动常微分方程的数值解法

Numerical Solution of Quasilinear Singularly Perturbed Ordinary Differential Equation without Turning Points

  • 摘要: 本文讨论二阶拟线性奇摄动常微分方程边值问题的数值解法.首先以一个非线性一阶初值问题近似原问题,然后用迭代法求解该近似问题.最后通过迭代法与古典格式得到一个比较满意的结果.
  • [1] Osher,S.,Nonlinear singular perturbation problems and one-sided difference schemes,SIAM J.Numer.Anal.,18,1(1981),129-144.
    [2] Niijima,K.,On a difference scheme of exponential type for a nonlinear singular perturbation problem,Numer.Math.,46(1985),521-539.
    [3] Niijima,K.,An error analysis for a difference scheme of exponential type applied to a nonlinear singular perturbation problem without turning points,J.Conip.Appl.Math.,15(1986),93-101.
    [4] Lorenz,J.,Combinations of initial and boundary value method for a class of singular perturbation problem,Numerical Analysis of Singular Perturbation Problem(eds.Hemker/Miller)(1979),296-315.
    [5] 林平,非线性二阶奇异摄动常微分方程的数值解(待发表).
    [6] Kadalbajoo,M.K.and Y.N.,Reddy,Initial-value technique for a class of nonlinear singular perturbation problems,J.Optim.Theory and Appls.,53,3(1987),395-406.
    [7] Sattinger,D.H.,Monotone methods in nonlinear elliptic and parabolic boundary value problems,Indiana Univ.Math.J.,21,11(1972),979-1000.
    [8] Howes,F.A.,Singular perturbations and differential inequalities.Memoirs of the AMS.5(1976),1-75.
    [9] 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).
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出版历程
  • 收稿日期:  1988-12-08
  • 刊出日期:  1989-11-15

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