关于两点边值问题配置解的组合方法

目前,在用组合校正方法提高两点边值问题配置解的精度方面,已有一些工作。例如,Manabu Sakai考虑了三次样条配置解而采用两种不同投影的组合;黄友谦考虑了三次样条配置解同差分解的组合;林群,刘嘉荃给出了配置解的外推方法。本文基于上述工作的思想,提出一种新的组合方法。即通过对三次样条配置解和二次样条配置解进

COMBINATION OF COLLOCATION SOLUTION FOR A TWO-POINT BOUNDARY VALUE PROBLEM

Let y_2 and y_3 represent respectively quadric and cubic spline solutions of a two-point boundary value problem, which are collocated at the Gauss points for the quadriccase and at the net points for the cubic case. Both approximate to the true solutionto the order O(h~2). Set y=2y_2--y_3. It is shown that y can attain a higher order O (h~4).