一种新型的四阶精度分段三次插值  

A new kind of piecewise cubic interpolation with fourth-order accuracy

作　　者：刘志方[1] 王同科[1] 王凤[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2014年第4期6-9,共4页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(41471001)

摘　　要：针对第一边界条件和周期边界条件的插值问题,给出了一种新的导数恢复格式,并用能量估计法证明了导数恢复格式按照离散L2范数具有四阶收敛精度.利用节点值和恢复出的导数值构造了一种新型的四阶精度分段三次插值函数.数值算例验证了理论分析的正确性和插值函数的实用性.The interpolation problem for the first boundary condition and the periodic boundary condition is considered, and a new derivative recovery scheme is derived. It is proved that the given scheme is convergent with fourth-order accuracy with respect to discrete L2 norm by using energy method. Then, a new kind of piecewise cubic interpolation with fourth-order accuracy is constructed by using the node values and the recovered derivative values. Numerical examples verify the correctness of the theoretical analvsis and the effectiveness of the scheme

关 键 词：三次插值 导数恢复格式 误差估计 四阶精度 

分 类 号：O241.4[理学—计算数学]