Barycentric rational collocation method for fractional reaction-diffusion equation

Jin Li; Jin Li

doi:10.3934/math.2023451

AIMS Mathematics

2023, Volume 8, Issue 4: 9009-9026. doi: 10.3934/math.2023451

Previous Article Next Article

Research article Special Issues

Barycentric rational collocation method for fractional reaction-diffusion equation

Jin Li ^,

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

Received: 22 December 2022 Revised: 29 January 2023 Accepted: 02 February 2023 Published: 10 February 2023
MSC : 65D32, 65D30, 65R20

Barycentric rational collocation method (BRCM) for solving spatial fractional reaction-diffusion equation (SFRDE) is presented. New Gauss quadrature with weight function $ (s_{\theta}-\tau)^{\xi-\alpha} $ is constructed to approximate fractional integral. Matrix equation of SFRDF is obtained from discrete SFRDE. With help of the error of barycentrix rational interpolation, convergence rate is obtained.
- linear barycentric rational interpolation,
- collocation method,
- fractional reaction-diffusion equation
Citation: Jin Li. Barycentric rational collocation method for fractional reaction-diffusion equation[J]. AIMS Mathematics, 2023, 8(4): 9009-9026. doi: 10.3934/math.2023451

Related Papers:

Abstract

Barycentric rational collocation method (BRCM) for solving spatial fractional reaction-diffusion equation (SFRDE) is presented. New Gauss quadrature with weight function $ (s_{\theta}-\tau)^{\xi-\alpha} $ is constructed to approximate fractional integral. Matrix equation of SFRDF is obtained from discrete SFRDE. With help of the error of barycentrix rational interpolation, convergence rate is obtained.

References

[1]	M. Abramowitz, I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, US Government Printing Office, 1948
[2]	F. Dell'Accio, F. Di Tommaso, G. Ala, E. Francomano, Electric scalar potential estimations for non-invasive brain activity detection through multinode Shepard method, 2022 IEEE 21st Mediterranean Electrotechnical Conference, 2022. https://doi.org/10.1109/MELECON53508.2022.9842881
[3]	I. T. Huseynov, A. Ahmadova, A. Fernandez, N. I. Mahmudov, Explicit analytical solutions of incommensurate fractional differential equation systems, Appl. Math. Comput., 390 (2021), 125590. https://doi.10.1016/j.amc.2020.125590 doi: 10.1016/j.amc.2020.125590
[4]	T. Jiang, X. Wang, J. Ren, J. Huang, J. Yuan, A high-efficient accurate coupled mesh-free scheme for 2D/3D space-fractional convection-diffusion/Burgersi problems, Comput. Math. Appl., 2022, https://doi.org/10.1016/j.camwa.2022.10.020
[5]	Y. Chen, Q. Li, H. Yi, Y. Huang, Immersed finite element method for time fractional diffusion problems with discontinuous coefficients, Comput. Math. Appl., 128 (2022), 121–129 https://doi.10.1016/j.camwa.2022.09.023 doi: 10.1016/j.camwa.2022.09.023
[6]	N. Srivastava, V. K. Singh, L3 approximation of Caputo derivative and its application to time-fractional wave equation, Math. Comput. Simul., 205 (2023), 532–557 https://doi.10.1016/j.matcom.2022.10.003 doi: 10.1016/j.matcom.2022.10.003
[7]	W. Bu, S. Shu, X. Yue, A. Xiao, W. Zeng, Space-time finite element method for the multi-term time-space fractional diffusion equation on a two-dimensional domain, Comput. Math. Appl., 78 (2019), 1367–1379 https://doi.10.1016/j.camwa.2018.11.033 doi: 10.1016/j.camwa.2018.11.033
[8]	S. Toprakseven, A weak Galerkin finite element method on temporal graded meshes for the multi-term time fractional diffusion equations, Comput. Math. Appl., 128 (2022), 108–120 https://doi.10.1016/j.camwa.2022.10.012 doi: 10.1016/j.camwa.2022.10.012
[9]	A. Ghafoor, N. Khan, M. Hussain, R. Ullah, A hybrid collocation method for the computational study of multi-term time fractional partial differential equations, Comput. Math. Appl., 128 (2022), 130–144 https://doi.10.1016/j.camwa.2022.10.005 doi: 10.1016/j.camwa.2022.10.005
[10]	P. Berrut, M. S. Floater, G. Klein, Convergence rates of derivatives of a family of barycentric rational interpolants. Appl. Numer. Math., 61, (2011), 989–1000. https://doi.10.1016/j.apnum.2011.05.001
[11]	J. 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.10.1137/120904020
[12]	M. S. Floater, K. Hormann, 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
[13]	G. Klein, J. 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
[14]	G. Klein, J. 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
[15]	R. Baltensperger, J. P. Berrut, The linear rational collocation method, J. Comput. Appl. Math., 134 (2001), 243–258. https://doi.org/10.1016/S0377-0427(00)00552-5 doi: 10.1016/S0377-0427(00)00552-5
[16]	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
[17]	J. Li, Y. Cheng, Linear barycentric rational collocation method for solving second-order Volterra integro-differential equation, Comput. Appl. Math., 39 (2020), 92. https://doi.org/10.1007/s40314-020-1114-z doi: 10.1007/s40314-020-1114-z
[18]	J. Li, Y. Cheng, Barycentric rational method for solving biharmonic equation by depression of order, Numer. Methods Partial Differ. Equations, 37 (2021), 1993–2007. https://doi.org/10.1002/num.22638 doi: 10.1002/num.22638
[19]	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
[20]	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
[21]	Z. Q. Wang, S. P. Li, Barycentric interpolation collocation method for nonlinear problems, National Defense Industry Press, 2015.
[22]	Z. Q. Wang, Z. K. Xu, J. Li, Mixed barycentric interpolation collocation method of displacement-pressure for incompressible plane elastic problems, Chin. J. Appl. Mech., 35 (2018), 195–201.
[23]	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
[24]	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
[25]	W. H. Luo, T. Z. Huang, X. M. Gu, Y. Liu, Barycentric rational collocation methods for a class of nonlinear parabolic partial differential equations, Appl. Math. Lett., 68 (2017), 13–19. https://doi.org/10.1016/j.aml.2016.12.011 doi: 10.1016/j.aml.2016.12.011
[26]	F. Delli'Accio, F. Di Tommaso, Rate of convergence of multinode shepard operators, Dolomit. Res. Notes Approx., 12 (2019), 1–6. https://doi.org/10.14658/pupj-drna-2019-1-1 doi: 10.14658/pupj-drna-2019-1-1
[27]	T. J. Rivlin, Chebyshev polynomials, Courier Dover Publications, 2020.
[28]	K. Jing, N. Kang, A convergent family of bivariate Floater-Hormann rational interpolants, Comput. Methods Funct. Theory, 21 (2021), 271–296. https://doi.org/10.1007/s40315-020-00334-9 doi: 10.1007/s40315-020-00334-9

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)