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Particle Swarm Optimization algorithm for Solving Singular Perturbed Problemsation Problems on Layer Adaptive Mesh

Published: 14 March 2022 Publication History

Abstract

A class of singularly perturbed convection diffusion problems is solved on bakhvalov Shishkin grid by combining particle swarm optimization with difference scheme. For the mesh parameters of bakhvalov Shishkin mesh, particle swarm optimization algorithm is used to optimize, and the objective function of minimum error norm is constructed. The numerical results of two examples show that compared with the fixed grid parameters, the particle swarm optimization algorithm can get better numerical results, and the numerical results have convergence, which verifies the effectiveness and superiority of the method.

References

[1]
T. Linss, “Lay er-adapted meshes for convection-diffusion problems,” Comput. Methods Appl. Mech. Engrg., vol. 192, pp. 1061-1105, 2003.
[2]
Y. Yin, P. Zhu, B. Wang, “Analysis of a Streamline-Diffusion Finite Element Method on Bakhvalov-Shishkin Mesh for Singularly Perturbed Problem,” Numerical Mathematics: Theory, Methods and Applications, vol. 010, no. 1, pp. 44-64, 2017.
[3]
W. K. Zahra, D. M. Van, “Discrete Spline Solution of Singularly Perturbed Problem with Two Small Parameters on a Shishkin-Type Mesh,” Computational Mathematics and Modeling, vol. 029, no. 3, pp. 367-381, 2018.
[4]
A. Das, S. Natesan, “Parameter-uniform numerical method for singularly perturbed 2D delay parabolic convection-diffusion problems on Shishkin mesh,” Journal of Applied Mathematics and Computing, vol. 059, pp. 207-225, 2019.
[5]
M. Brdar, H. Zarin, “A singularly perturbed problem with two parameters on a Bakhvalov-type mesh,” Journal of Computational and Applied Mathematics, vol. 292, pp. 307-319, 2016.
[6]
D. Shakti, J. Mohapatra, “Layer-adapted Meshes for Parameterized Singular Perturbation Problem,” Procedia Engineering, vol.127, pp. 539-544, 2015.
[7]
Z. Cen, J. Chen, L. Xi, “A second-order hybrid finite difference scheme for a system of coupled singularly perturbed initial value problems,” Journal of Computational & Applied Mathematics, vol. 234, no. 12, pp. 3445-3457, 2010.
[8]
R. C. Eberhart, J. Kennedy, “A new optimizer using particle swarm theory,” Proceedings of the Sixth International Sympo- sium on Micro Machine and Human Science. Nagoya: IEEE, pp. 39-43, 199.
  1. Particle Swarm Optimization algorithm for Solving Singular Perturbed Problemsation Problems on Layer Adaptive Mesh

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    cover image ACM Other conferences
    AIAM2021: 2021 3rd International Conference on Artificial Intelligence and Advanced Manufacture
    October 2021
    3136 pages
    ISBN:9781450385046
    DOI:10.1145/3495018
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    Published: 14 March 2022

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