含转向点的奇异摄动问题的二阶精度差分解法

A SECOND-ORDER ACCURATE DIFFERENCE METHOD FOR A SINGULARLY PERTURBED PROBLEM WITH THE TURNING POINT

对含转向点的两点边值问题Lu(x)≡ε″+ p(x)u′-q(x)u=f(x),-a<x<b,u(-a)= A,u(b)=B(a>0,b>0),Kellogg研究了p′(x)<0的情形得到了误差估计。Farrell研究了p(x)=xa,q(x)=b,a>0的情形,也得到了类似的结论。林鹏程,颜鹏翔改进了Kellogg的证明方法,证明了Il’in格式对上述问题(p(0)=0,p′(x)<0,q(x)≥β>0)具有一阶一致收敛性。

In this paper we conotruct a uniform second-order difference scheme for a singularly per-turbed two-point boundary value problem with the turning point. A numerical example isgiven. The numericial results show that the method is better than Il'in's scheme.