Czasopismo
2022
|
Vol. 55, nr 1
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574--586
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
The time-fractional cable model is solved using an extended cubic B-spline (ECBS) collocation strategy. The B-spline function was used for space partitioning, while the Caputo-Fabrizio (CF) was used for temporal discretization. The finite difference technique was used to discretize the CF operator. For the first time in cable modeling, the CF operator has been used. In terms of time, the convergence of order τ . An ECBS collocation approach is investigated by numerical example at different values, and comparisons with published work are made. The numerical results show that the scheme performed well, and the graphical representations show that the results are very close to exact values. The Von Neumann technique is applied to investigate the stability of the proposed scheme.
Czasopismo
Rocznik
Tom
Strony
574--586
Opis fizyczny
Bibliogr. 34 poz., tab., wykr.
Twórcy
autor
- Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, 31952 Al Khobar, Saudi Arabia , aiqbal@pmu.edu.sa
autor
- Department of Mathematics, COMSATS Institute of Information Technology, Lahore, 54000, Pakistan, tayyaba.akram2020@gmail.com
Bibliografia
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- [5] A. Atangana and B. S. T. Alkahtani, Extension of the resistance inductance, capacitance electrical circuit of fractional derivative without singular kernel, Adv. Mech. Eng. 7 (2015), no. 6, 1–6, DOI: https://doi.org/10.1177/1687814015591937.
- [6] J. F. Gómez-Aguilar, M. G. Lopez-Lopez, V. M. Alvarado-Martınez, J. Reyes-Reyes, and M. Adam-Medina, Modeling diffusive transport with a fractional derivative without singular kernel, Phys. A 447 (2016), 467–481, DOI: https://doi.org/10.1016/j.physa.2015.12.066.
- [7] S. Djennadi, N. Shawagfeh, M. S. Osman, J. F. Gómez-Aguilar, and O. A. Abu Arqub, The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique, Phys. Scr. 96 (2021), 094006, DOI: https://doi.org/10.1088/1402-4896/ac0867.
- [8] S. Momani, B. Maayah, and O. AbuArqub, The reproducing kernel algorithm for numerical solution of Van der Poldamping model in view of the Atangana-Baleanu fractional approach, Fractals 28 (2020), no. 8, 2040010, DOI: https://doi.org/10.1142/S0218348X20400101.
- [9] X. J. Yang, Z. Z. Zhang, and H. M. Srivastava, Some new applications for heat and fluid flows via fractional derivatives without singular kernel, Therm. Sci. 20 (2016), no. 3, 833–839, DOI: https://doi.org/10.2298/TSCI16S3833Y.
- [10] O. AbuArqub, Numerical simulation of time-fractional partial differential equations arising in fluid flows via reproducing Kernel method, Int. J. Numer. Meth. Heat. Fluid 30 (2020), no. 11, 4711–4733, DOI: https://doi.org/10.1108/HFF-10-2017-0394.
- [11] A. Atangana, On the new fractional derivative and application to nonlinear Fisher’s reaction-diffusion equation, Appl. Math. Comput. 273 (2016), 948–956, DOI: https://doi.org/10.1016/j.amc.2015.10.021.
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- [13] X. Y. Liu, Y. P. Liu, and Z. W. Wu, Optimization of a fractal electrode-level charge transport model, Therm. Sci. 25 (2021), no. 3B, 2213–2220, DOI: https://doi.org/10.2298/TSCI200301108L.
- [14] D. D. Dai, T. T. Ban, and Y. L. Wang, The piecewise reproducing kernel method for the time variable fractional order advection-reaction-diffusion equations, Therm. Sci. 25 (2021), no. 2B, 1261–1268, DOI: https://doi.org/10.2298/TSCI200302021D.
- [15] K. L. Wang and S. W. Yao, He’s fractional derivative for the evolution equation, Therm. Sci. 24 (2020), no. 4, 2507–2513, DOI: https://doi.org/10.2298/TSCI2004507W.
- [16] X. L. Hu and L. M. Zhang, Implicit compact difference schemes for the fractional cable equation, Appl. Math. Model. 36 (2012), no. 9, 4027–4043, DOI: https://doi.org/10.1016/j.apm.2011.11.027.
- [17] B. Yu and X. Y. Jiang, Numerical identification of the fractional derivatives in the two-dimensional fractional cable equation, J. Sci. Comput. 68 (2016), 252–272, DOI: https://doi.org/10.1007/s10915-015-0136-y.
- [18] Y. Y. Zheng and Z. G. Zhao, The discontinuous Galerkin finite element method for fractional cable equation, Appl. Numer. Math. 115 (2017), 32–41, DOI: https://doi.org/10.1016/j.apnum.2016.12.006.
- [19] X. Yang, X. Y. Jiang, and H. Zhang, A time-space spectral tau method for the time fractional cable equation and its inverse problem, Appl. Numer. Math. 130 (2018), 95–111, DOI: https://doi.org/10.1016/j.apnum.2018.03.016.
- [20] Y. Liu, Y. W. Du, H. Li, and J. F. Wang, A two-grid finite element approximation for a nonlinear time-fractional cable equation, Nonlinear Dyn. 85 (2016), 2535–2548, DOI: https://doi.org/10.1007/s11071-016-2843-9.
- [21] Y. Liu, Y. W. Du, H. Li, and J. F. Wang, Some second-order θ schemes combined with finite element method for nonlinear fractional cable equation, Numer. Algorithms 80 (2019), 533–555, DOI: https://doi.org/10.1007/s11075-018-0496-0.
- [22] P. Zhu, S. Xie, and X. Wang, Non-smooth data error estimates for FEM approximations of the time fractional cable equation, Appl. Numer. Math. 121 (2017), 170–184, DOI: https://doi.org/10.1016/j.apnum.2017.07.005.
- [23] T. Akram, M. Abbas, A. Ali, A. Iqbal, and D. Baleanu, A numerical approach of a time fractional reaction-diffusion model with a non-singular kernel, Symmetry 12 (2020), no. 10, 1653, DOI: https://doi.org/10.3390/sym12101653.
- [24] T. Akram, M. Abbas, M. B. Riaz, A. I. Ismail,and N. M. Ali, Development and analysis of new approximation of extended cubic B-spline to the non-linear time fractional Klein-Gordon equation, Fractals 28 (2020), no. 8, 2040039, DOI: https://doi.org/10.1142/S0218348X20400393
- [25] K. Zeynab and S. Habibollah, B-spline wavelet operational method for numerical solution of time-space fractional partial differential equations, Int. J. Wavelets Multiresolut Inf. Process 15 (2017), no. 4, 1750034, DOI: https://doi.org/10.1142/S0219691317500345.
- [26] B. P. Moghaddam and J. A.T. Machado, A stable three-level explicit spline finite difference scheme for a class of nonlinear time variable order fractional partial differential equations, Comput. Math. Appl. 36 (2017), no. 6, 1262–1269, DOI: https://doi.org/10.1016/j.camwa.2016.07.010.
- [27] X. Li, Numerical solution of fractional differential equations using cubic B-spline wavelet collocation method, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), no. 10, 3934–3946, DOI: https://doi.org/10.1016/j.cnsns.2012.02.009.
- [28] K. M. Saad, M. M. Khader, J. F. Gómez-Aguilar, and D. Baleanu, Numerical solutions of the fractional Fisher’s type equations with Atangana-Baleanu fractional derivative by using spectral collocation methods, Chaos, 29 (2019), 023116, DOI: https://doi.org/10.1063/1.5086771.
- [29] T. Akram, M. Abbas, and A. I. Ismail, An extended cubic B-spline collocation scheme for time fractional sub-diffusion equation, AIP Confer. Proc. 2184 (2019), 060017, DOI: https://doi.org/10.1063/1.5136449.
- [30] T. Akram, M. Abbas, and A. I. Ismail, Numerical solution of fractional cable equation via extended cubic B-spline, AIP Confer. Proc. 2138 (2019), 030004, DOI: https://doi.org/10.1063/1.5121041.
- [31] N. Moshtaghi and A. Saadatmandi, Numerical solution of time fractional cable equation via the Sinc-Bernoulli collocation method, J. Appl. Comput. Mech. 7 (2021), no. 4, 1916–1924, DOI: https://doi.org/10.22055/JACM.2020.31923.1940.
- [32] L. Pezza and F. Pittoli, A fractional spline collocation-Galerkin method for the time-fractional diffusion equation, Commun Appl. Ind. Math. 9 (2018), 104–120, DOI: https://doi.org/10.1515/caim-2018-0007.
- [33] E. Y. Tabriz, M. Lakestani, and M. Razzaghi, Study of B-spline collocation method for solving fractional optimal control problems, Trans. Ins. Meas. Cont. 43 (2021), 2425–2437, DOI: https://doi.org/10.1177/0142331220987537
- [34] C. De Boor, A Practical Guide to Splines, Springer-Verlag, New York, vol. 27, 1978, p. 325.
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).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-62657522-3234-4d9e-bd93-85b7ed11e803