边界层型问题的插值摄动解法
Interpolation Perturbation Method for Solving the Boundary Layer Type Problems
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摘要: 本文在文[1]的基础上用插值摄动法研究了最高阶导数乘以小参数的二阶常微分方程的定解问题。算例表明,本文方法计算过程简单,其精度甚至比多重尺度法的一级近似结果的精度还稍高一些。Abstract: In this paper,on the basis of Ref.[1],the author studies the boundary-value problems of the second-order differential eqs.,the highest order derivation of which contaisn the small parameters.Numerical examples show that the calculating process of this paper is quite simple and its accuracy is even higher than that of the multiple scales method(first order approximation).
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Key words:
- boundary layer type problem /
- interpolation /
- singular perturbation method
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[1] 袁镒吾,求一类非线性振动微分方程的近似解的新方法,力学与实践,1(1990), [2] 钱伟长主编,咤奇异摄动理论及其在力学中的应用》,科学出版社,(1981). [3] A. H.奈弗,《摄动方法》(王辅俊等译),上海科学技术出版社(1984), 150, 158 [4] A. H.奈弗,《摄动方法习题集》(宋家骕、戴世强译),上海翻译出版公司(1990). -
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