《摄动方法导引》、《摄动方法习题集》

两书是 A.H.Nayfeh 的 Introduction to PerturbationTech(?)ques(1981)和 Problems in Perturbation(1985)的中译本.《导引》由复旦大学宋家骕副教授翻译,《习题集》由宋家骕和上海市应用数学和力学研究所戴世强教授译出,上海翻译出版公司出版.当前摄动方法越来越受到国内外学术界的重视,应用日益广泛和深入,成为寻求现代科学和技术问题     

COMPUTER COMPUTATION OF THE METHOD OF MULTIPLE SCALES-DIRICHLET PROBLEM FOR A CLASS OF SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS

The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales .     

APPLICATION OF THE MODIFIED METHOD OF MULTIPLE SCALES TO THE BENDING PROBLEMS FOR CIRCULAR THIN PLATE AT VERY LARGE DEFLECTION AND THE ASYMPTOTICS OF SOLUTIONS(Ⅱ)

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关于常微分方程转点问题共振的必要条件

本文首先修正带有转点的常微分方程共振必要条件中的一些误解,然后给出推导共振必要条件序列的递推过程.     

关于具有转向点的一类常微分方程的边值问题

本文应用多重尺度法研究具有转向点的一类常微分方程的边值问题。避免了[1]中出现的悖理,以及[2 ]中关于确定任意常数的变分运算;构造出边值问题的解的一致有效渐近近似式.并研究了非共振的情形.     

关于含小参数的拟线性椭圆型方程的狄立克雷问题

本文研究最高阶导数项含小参数的拟线性椭圆型方程的狄立克雷问题,在退化方程的特征是曲线和区域是凸域的一般情形下,给出构造一致有效渐近解的方法,并证明当小参数是充分小时,狄立克雷问题的解是存在和唯一.     

ON THE BOUNDARY LAYER METHODS

In this paper,the defect of the traditionary bound-ary layer methods(including the method of matched as-ymptotic expansions and the method of Visik-Lyusternik)is noted.from those methods we can not construct theasymptotic expansion of boundary layer term substantial-ly.So the method of multiple scales is proposed forconstructing the asymptotic expansion of boundary layerterm,the reasonable result is obtained.Furthermore,we compare this method With the method used by Levin-son,and find that both methods give the same asympto-tic expansion of boundary layer term.but our method issimpler.Again.we apply this method to study some known workson singular perturbations.The limitations of thoseworks have been noted,and the asymptotic expansion ofsolution is constructed in general condition.     

ON THE UNIFORMLY VALID ASYMPTOTIC SOLUTION OF NON-LINEAR DIRICHLET PROBLEM

In this paper,Dirichlet problem for second order quasi-linear elliptic equation with a small parameter at highestderivatives is studied.In case degenerate equation has nosingular point and parameter εis sufficiently small,theexistence and uniqueness of solution are proved,and the uni-formly valid asymptotic solution is derived on the entire do-main.     

关于常微分方程非线性边值问题的奇异摄动

本文在采用比其他作者所取用的更弱的条件下,应用改进的多重尺度法,考察含小参数的常微分方程的非线性边值问题。证明了解的存在性,作出了渐近解,并应用较简单的方法,估计了余项,改进和拓广了文中的结果。     

On the Boundary Value Problems for a Class of Ordinary Differential Equations with Turning Points

In this paper we study the boundary value problems for a class of ordinary differential equations with turning points by the method of multiple scales.The paradox in[1]and the variational approach in[2]are avoided.The uniformly valid asymptotic approximations of solutions have been constructed.We also study the case which does not exhibit resonance.