打靶法在常微分方程边界层型奇异摄动问题中的应用

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Shooting Method in Singular Perturbation Problem of Ordinary Differential Eauations with boundary Layers

摘要: 用自适应步长积分格式结合打靶技巧,可以有效地求解比较困难的常微分方程边界层型奇异摄动问题.本文给出了若干计算实例,说明了这种方法应用于线性问题时的一次收敛性,以及应用于单端、双端边界层、转向点和多个边界层时的效果,特别是能方便地求出多解.最后并与习用的差分方法作了比较.

Abstract: By using the adaptive steplength integration scheme with a shooting iechnique a rather difficult singualr perturbation problem of ordinctry differential equations with houndary layers can be calculated effectivcly.Computing examples are given in this paper, which show the convergence within one iterdtion of the method in the case of a lintear problem, the efficiency of the method for many boundary lavers and turning points, especially the convenience in calculating muliple solutions. A compartson with traditional difference method is given at the end of this paper.

[1]	O'Malley, R.E.Jr., Introduction to Singular Perturhations. Academic Press, New York (1974).
[2]	Bender, C.M. and S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill, New York (1978).
[3]	Cole, J.D., Perturbation Methods in Applied Mathematics, Ginn, Bleisdel (1968).
[4]	Nayfeh, A.H., Perturbation Methods. Wiley, New York (1973).
[5]	Wasow, W., Asymptotic Expansion for Ordinary Differential Equations, Interscience Publishers, New York (1965).
[6]	Doolan, E.P., J.J.H. Miller and W.H.A. Schilders, Uniform Numerical Methods for Problems with Initial and Boundary Layers. Borle Borle Press, Dublin (1980).
[7]	Pearson, C.E., On non-linear ordinary differential equations of boundary layer type, J. Math. Phvs., 47 (1968), 351-358.
[8]	Keller, H., Numerical Methods for Two-Poinl Boundarv-value Problems, Blaisdell, London (1968).
[9]	Stoer,J.and R. Bulirsch, Einfuhrung in die numerische Mathematik 11, Springer-Verlag, Berlin (1978).
[10]	Hall, G. and J.M. Watt, Modern Numerical Methods for Ordinary Differential Equations, Clarendon Press, Oxford (1976).
[11]	Ling, F.H. and J.Y. Li, Two-way shooting method in nonlinear boundary value problems of ordinary differential equations with boundary layers, Proceedings of Tenth International Conference on Nonlinear Oscillations. Bulgaria, (1984), 678-681.
[12]	凌复华,非线性振动周期解的数值分析,应用数学和力学,4. 4 (1983),489-506.