| 一种新型的四阶精度分段三次插值 |
| |
| 引用本文： | 刘志方,王同科,王凤.一种新型的四阶精度分段三次插值[J].天津师范大学学报(自然科学版),2014,34(4):6-9. |
| |
| 作者姓名： | 刘志方 王同科 王凤 |
| |
| 作者单位： | 天津师范大学数学科学学院,天津,300387 |
| |
| 基金项目： | 国家自然科学基金资助项目 |
| |
| 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.
|
| 关 键 词： | 三次插值 导数恢复格式 误差估计 四阶精度 |
A new kind of piecewise cubic interpolation with fourth-order accuracy |
| |
| LIU Zhifang,WANG Tongke,WANG Feng.A new kind of piecewise cubic interpolation with fourth-order accuracy[J].Journal of Tianjin Normal University(Natural Science Edition),2014,34(4):6-9. |
| |
| Authors: | LIU Zhifang WANG Tongke WANG Feng |
| |
| Institution: | LIU Zhifang;WANG Tongke;WANG Feng;College of Mathematical Science,Tianjin Normal University; |
| |
| Abstract: | 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 |
| |
| Keywords: | cubic interpolation derivative recovery scheme error estimate fourth-order accuracy |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
