二阶线性常微分方程张力样条配置解的渐近表示及其外推

Asymptotic Expression and Extrapolation of Tension Spline Collocation for Two-point Boundary Value Problem of Second-order Linear Ordinary Differential Equation

设u″（x）+p（x）u′（x）+q（x）u（x）=f（x） a≤x≤bu（a）=ua u（b）=ub （1）其中p（x）,q（x）∈c3[a,b],f（x）∈c3[a,b],q（x）≤q0<0或q（x）≥q1>0,由常微分方程基本理论知存在唯一的u（x）∈c5[a,b]满足（1）.又设△是[a。

Tension spline collocation for two-point boundary value problems of second-order linear ordinary differential equation are discussed.Asymptotic expressionsof error are also obtained.By using these asymptotic expressions,Richardsonextrapolation can be done and accuracy of solution can be improved.Numericalresults agree with theory.