摘要
将高阶数值微分问题等价转化为第一类积分方程的求解问题,本文给出了高阶数值微分的积分方程方法.利用Lavrentiev正则化方法求解积分方程,我们分析了正则化解的稳定性,给出正则化参数的先验、后验选取策略及相应正则化解的误差估计.最后,通过数值算例说明了积分方程方法求解高阶数值微分问题的数值有效性.
By reformulating the higher order numerical differentiation problem as an integral equation of the first kind, we give the integral equation method for the higher order numerical differentiation. Solving the integral equation by the Lavrentiev regularization method, we analysis the stability of the regularization solution, give the a-priori and a-posteriori choice strategies of the regularization parameter, and the error estimate of the regularization solution. Finally, the numerical validity of the integral equation method is shown by numerical examples.
出处
《赣南师范大学学报》
2017年第6期7-12,共6页
Journal of Gannan Normal University
基金
国家自然科学基金项目(11661008)
江西省自然科学基金项目(20161BAB211025)
江西省教育厅科技项目(GJJ150982)
江西省教育科学规划课题(16YB128)
关键词
数值微分
积分方程
正则化方法
正则化参数
误差估计
numerical differentiation
integral equation
regularization method
regularization parameter
error estimate
