Linear barycentric rational collocation method for solving biharmonic equation

• Autorzy: Li Jin

Identyfikatory

DOI

10.1515/dema-2022-0151

• Języki publikacji: EN

Abstrakty

EN

Two-dimensional biharmonic boundary-value problems are considered by the linear barycentric rational collocation method, and the unknown function is approximated by the barycentric rational polynomial. With the help of matrix form, the linear equations of the discrete biharmonic equation are changed into a matrix equation. From the convergence rate of barycentric rational polynomial, we present the convergence rate of linear barycentric rational collocation method for biharmonic equation. Finally, several numerical examples are provided to validate the theoretical analysis.

Słowa kluczowe

EN

linear barycentric rational; collocation method; error function; biharmonic equation; equidistant nodes; Chebyshev nodes

PL

metoda kolokacji; równanie biharmoniczne; węzły Czebyszewa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 587--603
• Opis fizyczny: Bibliogr. 24 poz., tab., wykr.

Twórcy

autor

Li Jin

• School of Science, Shandong Jianzhu University, Jinan 250101, P. R. China

Bibliografia

• [1] A. Cardone, D. Conte, R. D’ambrosio, and B. Paternoster, Multivalue collocation methods for ordinary and fractional differential equations, Mathematics 10 (2022), no. 2, 185, DOI: https://doi.org/10.3390/math10020185.
• [2] J. Shen, T. Tang, and L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer, New York, 2011.
• [3] J. P. Berrut, S. A. Hosseini, and G. Klein, The linear barycentric rational quadrature method for Volterra integral equations, SIAM J. Sci. Comput. 36 (2014), no. 1, 105–123, DOI: https://doi.org/10.1137/120904020.
• [4] P. Berrut and G. Klein, Recent advances in linear barycentric rational interpolation, J. Comput. Appl. Math. 259 (2014), 95–107, DOI: https://doi.org/10.1016/j.cam.2013.03.044.
• [5] E. Cirillo and K. Hormann, On the Lebesgue constant of barycentric rational Hermite interpolants at equidistant nodes, J. Comput. Appl. Math. 349 (2019), 292–301, DOI: https://doi.org/10.1016/j.cam.2018.06.011
• [6] A. Abdi, J. P. Berrut, and S. A. Hosseini, The linear barycentric rational method for a class of delay Volterra integro-differential equations, J. Sci. Comput. 75 (2001), 1757–1775, DOI: https://doi.org/10.1007/s10915-017-0608-3.
• [7] J. Li and Y. Cheng, Linear barycentric rational collocation method for solving second-order Volterra integro-differential equation, Comput. Appl. Math. 39 (2020), 92, DOI: https://doi.org/10.1007/s40314-020-1114-z.
• [8] M. Li and C. Huang, The linear barycentric rational quadrature method for auto-convolution Volterra integral equations, J. Sci. Comput. 78 (2019), no. 1, 549–564, DOI: https://doi.org/10.1007/s10915-018-0779-6.
• [9] J. Y. Lee and L. Greengard, A fast adaptive numerical method for stiff two-point boundary value problems, SIAM J. Sci. Comput. 18 (1997), no. 2, 403–429, DOI: https://doi.org/10.1137/S1064827594272797.
• [10] N. R. Bayramov and J. K. Kraus, On the stable solution of transient convection-diffusion equations, J. Comput. Appl. Math. 280 (2015), no. 1, 275–293, DOI: https://doi.org/10.1016/j.cam.2014.12.001.
• [11] J. Li and Y. Cheng, Linear barycentric rational collocation method for solving heat conduction equation, Numer. Methods Partial Differ. Equ. 37 (2021), no. 1, 533–545, DOI: https://doi.org/10.1002/num.22539.
• [12] M. S. Floater and K. Hormann, Barycentric rational interpolation with no poles and high rates of approximation, Numer. Math. 107 (2007), no. 2, 315–331, DOI: https://doi.org/10.1007/s00211-007-0093-y.
• [13] J. P. Berrut, M. S. Floater, and G. Klein, Convergence rates of derivatives of a family of barycentric rational interpolants, Appl. Numer. Math. 61 (2011), no. 9, 989–1000, DOI: https://doi.org/10.1016/j.apnum.2011.05.001.
• [14] G. Klein and J. P. Berrut, Linear rational finite differences from derivatives of barycentric rational interpolants, SIAM J. Numer. Anal. 50 (2012), no. 2, 643–656, DOI: https://doi.org/10.1137/110827156.
• [15] G. Klein and J. P. Berrut, Linear barycentric rational quadrature, BIT Numer. Math. 52 (2012), 407–424, DOI: https://doi.org/10.1007/s10543-011-0357-x.
• [16] S. Li and Z. Wang, High Precision Meshless barycentric Interpolation Collocation Method-Algorithmic Program and Engineering Application, Science Publishing, Beijing, 2012.
• [17] Z. Wang and S. Li, Barycentric Interpolation Collocation Method for Nonlinear Problems, National Defense Industry Press, Beijing, 2015.
• [18] Z. Wang, Z. Xu, and J. Li, Mixed barycentric interpolation collocation method of displacement-pressure for incompressible plane elastic problems, Chinese J. Appl. Mech. 35 (2018), no. 3, 195–201.
• [19] Z. Wang, L. Zhang, Z. Xu, and J. Li, Barycentric interpolation collocation method based on mixed displacement-stress formulation for solving plane elastic problems, Chinese J. Appl. Mech. 35 (2018), no. 2, 304–309.
• [20] M. L. Zhuang, C. Q. Miao, and S. Y. Ji, Plane elasticity problems by barycentric rational interpolation collocation method and a regular domain method, Internat. J. Numer. Methods Engrg. 121 (2020), no. 18, 4134–4156, DOI: https://doi.org/10.1002/nme.6431
• [21] J. Li, X. Su, and J. Qu, Linear barycentric rational collocation method for solving telegraph equation, Math. Method. Appl. Sci. 44 (2021), no. 14, 11720–11737, DOI: https://doi.org/10.1002/mma.7548.
• [22] J. Li and S. Yu, Linear barycentric rational collocation method for Beam force vibration equation, Shock. Vib. 2021 (2021), 5584274, DOI: https://doi.org/10.1155/2021/5584274.
• [23] N. Mai-Duy and R. I. Tanner, A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems, J. Comput. Appl. Math. 201 (2007), no. 1, 30–47, DOI: https://doi.org/10.1016/j.cam.2006.01.030.
• [24] J. Li and Y. Cheng, Barycentric rational method for solving biharmonic equation by depression of order, Numer. Methods Partial Differ. Equ. 37 (2021), no. 3, 1993–2007, DOI: https://doi.org/10.1002/num.22638.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).