Numerical differentiation for two-dimensional scattered data on arbitrary domain base on Hermite extension with an implicit iteration process

AIMS Mathematics

Benxue Gong¹  Zhenyu Zhao¹  Yingmei Wang¹  Tiao Bian² 

[1] 1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255049, China;2. Shandong Gpcmarket Info Tech Co., Ltd, Weifang, 261000, China;

关键词: numerical differentiation;    ill posed problem;    regularization;    implicit iteration;    hermite extension;   

DOI  :  10.3934/math.2022334

来源: DOAJ

【 摘 要 】

In this paper, we develop a method for numerical differentiation of two-dimensional scattered input data on arbitrary domain. A Hermite extension approach is used to realize the approximation and a modified implicit iteration method is proposed to stabilize the approximation process. For functions with various smooth conditions, the numerical solution process of the method is uniform. The error estimates are obtained and numerical results show that the new method is effective. The advantage of the method is that it can solve the problem in any domain.

【 授权许可】

Unknown