【摘要】 利用奇摄动理论,讨论了一类拟线性奇摄动边值问题。首先分别求得问题的外部解和内部解,再进行变量间的变换,得到外部解的内展开式和内部解的外展开式,利用边值条件和匹配原则,得出了该问题解的渐近展开式,推广了相应结论,并将所得结果应用于例子的求解。比较所得的渐近解和用边界层校正法求的解,可知所得到的渐近解达到了较高的精度。更多还原

【Abstract】 Using the theory of singularly perturbation,boundary problems of a class of quasilinear singularly perturbation are discussed.First,the internal and outer solutions of original problem are obtained,then substitution is carried between the variables to obtain the interior expansion of outer expansion and the outer expansion of the interior expansion.Finally,by matching theory and boundary value condition,the approximate expansions of solution for the problem are obtained,and the correspondent results are popularized and the results are applied to solving the problem.We know that the approximate achieves the higher accuracy,comparing the solution gotten by the approximate solution and the boundary layer correcting method.更多还原