摘要
讨论了一类三阶微分方程奇摄动边值问题.根据奇摄动理论得知问题的解在左边界点邻近具有非一致性.为构造一致有效的渐近解,利用多重尺度法,引进一个适当的快变量,把原来单个自变量的常微分方程转化为两个尺度变量的偏微分方程,再将解按两尺度变量展开成幂级数形式,并将这个幂级数展开式代入原问题的方程中,合并同量级的系数并令其为零,再利用原问题的边界条件和关于小参数的渐近展开原理及消去长期项的办法,可依次决定各待定量,从而克服了原问题解的展开式的非一致收敛性.最后得到了关于原三阶微分方程边值问题的一阶小量的一致有效的渐近解.
This paper discusses a class of singularly perturbed boundary value problem of the third order differential equation. According to the singularly perturbed theory, the solution presents non- uniformly convergence beside the left boundary. To create a uniformly valid asymptotic solution, it is advisable to introduce an adequate faster variable with multiple scale method, transforming the original single independent variable differential equation into a partial differential equation （PDE） with double - scale variables, and then expend the solution into power series with double - scale variables, which can be applied in the original equation and combined with coefficient of the same order, making it into zero. With the original boundary conditions and the theory of asymptotic expansion of small parameters as well as the method of avoided secular terms, each variable to be confirmed is to overcome the non - uniformly convergence in the expansion equations of the original solution, thus obtaining a uniformly valid asymptotic solution for the first small measurement of the third original order differential equation boundary value problem.
出处
《湖州师范学院学报》
2009年第1期38-40,共3页
Journal of Huzhou University
关键词
边值问题
两变量
渐近解
boundary value problem
two variables
asymptotic solution
