基于时间分数阶扩散方程源项反演的一阶与二阶数值微分方法

• 作者: 张文 王泽文 阮周生 陈树立
• 来源期刊: 高等学校计算数学学报
• 学科: 数学
• 年，卷（期）: 2019,（3）
• 页码范围: 244-264
• 页数: 21页
• 分类号: O242.2
• 语种: 中文

摘要

In this article,we consider the classically ill-posed problem of numerical differentiation in the framework of the PDEs-based numerical differentiation methods.A novel scheme for the first and second order numerical derivatives is proposed by the approach of an inverse source problem for a time-fractional diffusion equation.The numerical differentiation problem is transformed into the inverse source problem which induces a regularized optimization problem.The convergence rates of regularization solutions are derived under the a priori and a posteriori strategies for selecting regularization parameters,respectively.Finally,several examples are given to verify the efficiency and stability of the proposed scheme.

作者信息

序号	姓名	单位	发文数	被引次数	H指数	G指数
1	阮周生		17	49	5.0	6.0
2	张文		37	267	9.0	14.0
3	王泽文		54	335	11.0	15.0
4	陈树立		2	0	0.0	0.0