微分差分方程组边值问题的算法研究

The Algorithm Study of Bourdary Value Problem for a Differential-Difference Equation System

本文给出了如下微分差分方程组边值问题(P_ε):y′(x,ε)=a_1(x)y(x,ε)+b_1(x)z(x,ε)+c_1(x)y(x-1,ε)+d_1(x)z(x-1,ε)+φ_1(x)(0<x<l)εz′(x,ε)=a_2(x)y(x,ε)+b_2(x)z(x,ε)+c_2(x)y(x-1,ε)+d_2(x)z(x-1,ε)+φ_2(x)y(x,ε)=φ_1(x) z(x,ε)=φ_2(x) (-1≤x<0)y(0,ε)=φ_1(0) y(l,ε)=v (0<ε<<1)其中,a_i(x),b_i(x),c_i(x),d_i(x),φ_i(x),φ_i(x) i=1,2为光滑函数,上式的解直到 O(ε)阶的一致有效表达式.

In this paper,the BVP of D-D equation system as below is studied. (?)y'(x,ε)=α_1(x)y(x,ε)+b_1(x)z(x,ε)+c_1(x)y(x-1,ε)+d_1(x)z(x-1,ε)+φ_1(x) εz'(x,ε)=α_2(x)y(x,ε)+b_2(x)z(x,ε)+c_2(x)y(x-1,ε)+d_2(x)z(x-1,ε)+φ_2(x) (0<x<1) y(x,ε)=φ_1(x) z(x,ε)=φ_2(x) (-1≤x<0) y(0,ε)=φ_1(0) y(1,ε)=v Where α_i(x),b_i(x),c_i(x),d_i(x),φ_i(x),φ_i(x)(i=1,2)are smooth functions and e is a small parameter.We obtain a solution of uniformly valid asymptotic expansion.