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

Benxue Gong; Zhenyu Zhao; Tiao Bian; Yingmei Wang; Benxue Gong; Zhenyu Zhao; Tiao Bian; Yingmei Wang

doi:10.3934/math.2022334

AIMS Mathematics

2022, Volume 7, Issue 4: 5991-6015. doi: 10.3934/math.2022334

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Research article

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

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

Received: 19 August 2021 Revised: 13 December 2021 Accepted: 04 January 2022 Published: 14 January 2022
MSC : 47A52, 65D25

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.
- numerical differentiation,
- ill posed problem,
- regularization,
- implicit iteration,
- Hermite extension
Citation: Benxue Gong, Zhenyu Zhao, Tiao Bian, Yingmei Wang. Numerical differentiation for two-dimensional scattered data on arbitrary domain base on Hermite extension with an implicit iteration process[J]. AIMS Mathematics, 2022, 7(4): 5991-6015. doi: 10.3934/math.2022334

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Abstract

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.

References

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