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

作　　者：王国英[1] 

机构地区：[1]南京大学

出　　处：《数值计算与计算机应用》1990年第1期19-26,共8页Journal on Numerical Methods and Computer Applications

摘　　要：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.

关 键 词：边值问题 奇异摄动 有限元法 差分 

分 类 号：O175[理学—数学]