一类奇异方程边值问题样条差分格式的误差界

Error Bounds for Spline Finite Difference of Singular Two-point Boundary Value Problems

本文我们讨论了一类奇异方程x^(-a)(x^au′)′=f(x,u),u(0)=A或u′,(0)=0,u(1)=B,a=1,给出了这类方程的样条差分格式,证明了此格式具有二阶收敛性,并给出了一些数值例子。

In this paper, the author discusses the convergence of spline finite difference for a class of singular two-point boundary value problem x^(-α)(x~αu')'=f(x,u), u(0)=A, u(1) = B, α= 1. The boundary conditions may also be of the form u'(0) =0, u(1)=B. We prove that the spline finite difference method is a second-order method and give some numerical examples to illustrate this theory.