第一类算子方程的Hermite数值解

HERMITE NUMERICAL SOLUTION OF FIRST KIND OPERATOR EQUATION

应用Ｗ２２空间中的再生核，构造了一种求第一类算子方程Ａｕ＝ｆ的Ｈｅｒｍｉｔｅ数值解ｕ２ｎ的新方法。证明了当节点系在［ａ，ｂ］中稠密时，ｕ２ｎ（ｘ）一致收敛到方程的解析解ｕ（ｘ）。ｕ′２ｎ（ｘ）一致收敛到ｕ′（ｘ），并且误差按空间范数单调下降。

By the use of reproducing kernel of W 2 2, a new method for finding the hermite numerical solution u 2n (x) of the first kind operator equation Au=f is constructed. It is also proved that u 2n (x) uniformly converge to the analytic solution u (x) of the equation, u′ 2n (x) uniformly converge to u′(x) as the nodes become dense in a,b ; furthermore, the error decreases monotonically in the sense of space norm.