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Mathematical Biosciences and Engineering

2023, Volume 20, Issue 5: 8337-8357. doi: 10.3934/mbe.2023365
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Linear barycentric rational collocation method to solve plane elasticity problems

  • School of Science, Shandong Jianzhu University, Jinan 250101, China

  • Academic Editor: Feliz Minhós
  • Received: 07 December 2022 Revised: 22 February 2023 Accepted: 24 February 2023 Published: 02 March 2023

  • A linear barycentric rational collocation method for equilibrium equations with polar coordinates is considered. The discrete linear equations is changed into the matrix forms. With the help of error of barycentrix polar coordinate interpolation, the convergence rate of the linear barycentric rational collocation method for equilibrium equations can be obtained. At last, some numerical examples are given to valid the proposed theorem.

    Citation: Jin Li. Linear barycentric rational collocation method to solve plane elasticity problems[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 8337-8357. doi: 10.3934/mbe.2023365

    Related Papers:

  • A linear barycentric rational collocation method for equilibrium equations with polar coordinates is considered. The discrete linear equations is changed into the matrix forms. With the help of error of barycentrix polar coordinate interpolation, the convergence rate of the linear barycentric rational collocation method for equilibrium equations can be obtained. At last, some numerical examples are given to valid the proposed theorem.


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    [1] L. J. Qiao, W. L. Qiu, B. Tang, A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation, Numer. Methods Partial Differ. Equations, 39 (2023), 1333–1354, https://doi.org/10.1002/num.22936 doi: 10.1002/num.22936
    [2] Z. J. Fu, Z. C. Tang, Q. Xi, Q. G. Liu, Y. Gu, F. J. Wang, Localized collocation schemes and their applications, Acta Mech. Sin., 38 (2022), 422167. https://doi.org/10.1007/s10409-022-22167-x doi: 10.1007/s10409-022-22167-x
    [3] Z. J. Fu, Q. Xi, Y. Gu, J. P. Li, W. Z. Qu, L. L. Sun, et al., Singular boundary method: a review and computer implementation aspects, Eng. Anal. Boundary Elem., 147 (2023), 231–266. https://doi.org/10.1016/j.enganabound.2022.12.004 doi: 10.1016/j.enganabound.2022.12.004
    [4] Y. P. Chen, X. Zhao, Y. Q. Huang, Mortar element method for the time dependent coupling of stokes and darcy flows, J. Sci. Comput., 80 (2019), 1310–1329. https://doi.org/10.1007/s10915-019-00977-4 doi: 10.1007/s10915-019-00977-4
    [5] X. X. Lin, Y. P. Chen, Y. Q. Huang, A posteriori error estimates of hp spectral element methods for optimal control problems with L-2-norm state constraint, Numerical Algorithms, 83 (2020), 1145–1169. https://doi.org/10.1007/s11075-019-00719-5 doi: 10.1007/s11075-019-00719-5
    [6] C. H. Yao, F. R. Li, Y. M. Zhao, Superconvergence analysis of two-grid FEM for Maxwell's equations with a thermal effect, Comput. Math. Appl., 79 (2020), 378–3393. https://doi.org/10.1016/j.camwa.2020.02.001 doi: 10.1016/j.camwa.2020.02.001
    [7] C. H. Yao, Z. Y. Wang, Y. M. Zhao, A leap-frog finite element method for wave propagation of Maxwell-Schrodinger equations with nonlocal effect in metamaterials, Comput. Math. Appl., 90 (2021), 25–37. https://doi.org/10.1016/j.camwa.2021.02.019 doi: 10.1016/j.camwa.2021.02.019
    [8] J. Shen, T. Tang, L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer, 2011. https://doi.org/10.1007/978-3-540-71041-7
    [9] L. N. Trefethen, Spectral Methods in MATLAB, SIAM, 2000. https://doi.org/10.1137/1.9780898719598
    [10] F. Dell'Accio, F. Di Tommaso, O. Nouisser, N. Siar, Solving Poisson equation with Dirichlet conditions through multinode Shepard operators, Comput. Math. Appl., 98 (2021), 254–260. https://doi.org/10.1016/j.camwa.2021.07.021 doi: 10.1016/j.camwa.2021.07.021
    [11] F. Dell'Accio, F. Di Tommaso, G. Ala, E. Francomano, Electric scalar potential estimations for non-invasive brain activity detection through multinode Shepard method, in 2022 IEEE 21st Mediterranean Electrotechnical Conference (MELECON), 2022, 1264–1268. https://doi.org/10.1109/MELECON53508.2022.9842881
    [12] P. Berrut, S. A. Hosseini, G. Klein, The linear barycentric rational quadrature method for Volterra integral equations, SIAM J. Sci. Comput., 36 (2014), 105–123. https://doi.org/10.1137/120904020 doi: 10.1137/120904020
    [13] J. P. Berrut, G. Klein, Recent advances in linear barycentric rational interpolation, J. Comput. Appl. Math., 259 (2014), 95–107. https://doi.org/10.1016/j.cam.2013.03.044 doi: 10.1016/j.cam.2013.03.044
    [14] E. Cirillo, H. Kai, On the Lebesgue constant of barycentric rational Hermite interpolants at equidistant nodes, J. Comput. Appl. Math., 349 (2019), 292–301. https://doi.org/10.1016/j.cam.2018.06.011 doi: 10.1016/j.cam.2018.06.011
    [15] M. S. Floater, H. Kai, Barycentric rational interpolation with no poles and high rates of approximation, Numer. Math., 107 (2007), 315–331. https://doi.org/10.1007/s00211-007-0093-y doi: 10.1007/s00211-007-0093-y
    [16] S. De Marchi, F. Dell'Accio, M. Mazza, On the constrained mock Chebyshev least-squares, J. Comput. Appl. Math., 280 (2015), 94–109. https://doi.org/10.1016/j.cam.2014.11.032 doi: 10.1016/j.cam.2014.11.032
    [17] F. Dell'Accio, F. Di Tommaso, F. Nudo, Generalizations of the constrained mock-Chebyshev least squares in two variables: tensor product vs total degree polynomial interpolation, Appl. Math. Lett., 125 (2022), 107732. https://doi.org/10.1016/j.aml.2021.107732 doi: 10.1016/j.aml.2021.107732
    [18] F. Dell'Accio, F. Di Tommaso, F. Nudo, Constrained mock-Chebyshev least squares quadrature, Appl. Math. Lett., 134 (2022), 108328. https://doi.org/10.1016/j.aml.2022.108328 doi: 10.1016/j.aml.2022.108328
    [19] A. Abdi, J. P. Berrut, S. A. Hosseini, The linear barycentric rational method for a class of delay Volterra integro-differential equations, J. Sci. Comput., 75 (2018), 1757–1775. https://doi.org/10.1007/s10915-017-0608-3 doi: 10.1007/s10915-017-0608-3
    [20] J. P. Berrut, S. F. Michael, G. Klein, Convergence rates of derivatives of a family of barycentric rational interpolants, Appl. Numer. Math., 61 (2011), 989–1000. https://doi.org/10.1016/j.apnum.2011.05.001 doi: 10.1016/j.apnum.2011.05.001
    [21] G. Klein, J. P. Berrut, Linear rational finite differences from derivatives of barycentric rational interpolants, SIAM J. Numer. Anal., 50 (2012), 643–656. https://doi.org/10.1137/110827156 doi: 10.1137/110827156
    [22] G. Klein, J. P. Berrut, Linear barycentric rational quadrature, BIT Numer. Math., 52 (2012), 407–424. https://doi.org/10.1007/s10543-011-0357-x doi: 10.1007/s10543-011-0357-x
    [23] J. Li, Y. Cheng, Linear barycentric rational collocation method for solving second-order Volterra integro-differential equation, Comput. Appl. Math., 39 (2020). https://doi.org/10.1007/s40314-020-1114-z doi: 10.1007/s40314-020-1114-z
    [24] S. Li, Z. Wang, High Precision Meshless Barycentric Interpolation Collocation Method–Algorithmic Program and Engineering Application, Science Publishing, Beijing, 2012.
    [25] Z. Wang, Z. Xu, J. Li, Mixed barycentric interpolation collocation method of displacement-pressure for incompressible plane elastic problems, Chin. J. Appl. Mech., 35 (2018), 195–201.
    [26] Z. Wang, L. Zhang, Z. Xu, J. Li, Barycentric interpolation collocation method based on mixed displacement-stress formulation for solving plane elastic problems, Chin. J. Appl. Mech., 35 (2018), 304–309. https://doi.org/10.11776/cjam.35.02.D002 doi: 10.11776/cjam.35.02.D002
    [27] Z. Wang, S. Li, Barycentric Interpolation Collocation Method for Nonlinear Problems, National Defense Industry Press, Beijing, 2015.
    [28] J. Li, Y. Cheng, Linear barycentric rational collocation method for solving heat conduction equation, Numer. Methods Partial Differ. Equations, 37 (2021), 533–545. https://doi.org/10.1002/num.22539 doi: 10.1002/num.22539
    [29] J. Li, X. Su, J. Qu, Linear barycentric rational collocation method for solving telegraph equation, Math. Methods Appl. Sci., 44 (2021), 11720–11737. https://doi.org/10.1002/mma.7548 doi: 10.1002/mma.7548
    [30] J. Li, Linear barycentric rational collocation method for solving biharmonic equation, Demonstr. Math., 55 (2022), 587–603. https://doi.org/10.1515/dema-2022-0151 doi: 10.1515/dema-2022-0151
    [31] J. Li, X. Su, K. Zhao, Barycentric interpolation collocation algorithm to solve fractional differential equations, Math. Comput. Simul., 205 (2023), 340–367. https://doi.org/10.1016/j.matcom.2022.10.005 doi: 10.1016/j.matcom.2022.10.005
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