一类奇异摄动初值问题的数值渐近解  

Numerical asymptotic solutions to a class of singularly perturbed initial value problems

作　　者：彭翼[1] 朱升峰[1] 

机构地区：[1]华东师范大学数学系,上海200241

出　　处：《应用数学与计算数学学报》2013年第3期363-371,共9页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金青年科学基金资助项目(11201153);中央高校基本科研业务费专项资金资助项目

摘　　要：奇异摄动理论和方法中的渐近理论对非线性的复杂方程在无法求出其精确解的前提下,通过构造出一致有效的渐近解,为解决这类问题提供了有力的工具,其中边界层函数法是最行之有效的方法之一.结合边界层函数法和数值方法,构造出了零级数值渐近解,为进一步求解正则级数和边界层级数的各项系数奠定了基础.Under the premise that the exact solutions of nonlinear equations can not be obtained, the asymptotic theory in the singular perturbation theory and methods provides a powerful tool by constructing a uniformly valid asymptotic solution for solving such problems. The boundary layer function method is one of the most effective ways. The boundary layer function approach with numeri- cal methods to construct a zero-order numerical asymptotic solution is combined, which establishes a basis for obtaining further the coefficients in the regular series and boundary layer series.

关 键 词：奇异摄动 初值问题 渐近理论 边界层函数法 数值渐近解 

分 类 号：O175.8[理学—数学]