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Numerical identification of the fractal orders in the generalized nonlocal elastic model

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Abstract

This article deals with numerical solution and identification of the fractal orders for the generalized nonlocal elastic model. Based on the collocation-finite difference scheme for the forward operator, a regularized method is proposed for solving of the forward problem with the aid of Tikhonov regularization. This method is non-iterative and independent of preconditioning of the coefficient matrix, which gives a simple and direct approach to numerical solution of the nonlocal elastic model. The identification problem of determining the fractal orders is solved by using the optimal perturbation algorithm with additional observations at some measurable points. The inversion solutions with noisy data give good approximations to the exact orders demonstrating the validity of the numerical algorithms.

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Acknowledgements

This work is supported by the National Natural Science Foundation, China (No.11871313), the Natural Science Foundation of Shandong Province (No.ZR2019MA021), and the 2018 doctoral research innovation foundation of Inner Mongolia Autonomous Region, China.

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Authors and Affiliations

  1. College of Science, Inner Mongolia University of Technology, Hohhot, 010100, Inner Mongolia, China

    Guangsheng Chi

  2. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, Shandong, China

    Gongsheng Li

Authors
  1. Guangsheng Chi
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  2. Gongsheng Li
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Contributions

GC carried out all the numerical computations and the numerical inversions, and provided the figures and tables in the manuscript. GL put forward the identification problem and wrote the main manuscript text. Both of the authors reviewed the manuscript.

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Correspondence to Gongsheng Li.

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Chi, G., Li, G. Numerical identification of the fractal orders in the generalized nonlocal elastic model. J Eng Math 142, 4 (2023). https://doi.org/10.1007/s10665-023-10285-4

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