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The method based on quintic B-spline functions for addressing time-fractional advection-dispersion equations | ||
| Journal of Mathematical Modeling | ||
| دوره 14، شماره 2، مرداد 2026، صفحه 533-556 اصل مقاله (836.48 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2025.31501.2833 | ||
| نویسندگان | ||
| Mohamed Adel1؛ Somayieh Abdi-mazraeh2؛ Golamreza Zaki2؛ Safar Irandust-Pakchin* 3 | ||
| 1Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, KSA. | ||
| 2Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran | ||
| 3Department of Mathematics | ||
| چکیده | ||
| This paper introduces a numerical method designed to address the fractional time advection-dispersion equation. Initially, the time dimension is discretized by employing the L1 method. Subsequently, quintic B-spline functions are utilized for the discretization of the spatial dimension. This approach yields a system of algebraic equations that can be efficiently solved. The proposed method is proven to be unconditionally stable. Numerical experiments provide compelling evidence of the method’s efficiency and effectiveness | ||
| کلیدواژهها | ||
| Advection-dispersion equation؛ Caputo fractional derivative؛ quintic B-spline functions | ||
| مراجع | ||
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[1] A.H. B. Albohiwela, S. Irandoust-Pakchin, A.J. Akbarfam, Optimal collocation method for time fractional advection–dispersion equation using modified generalized Laguerre polynomials and particle swarm optimization algorithm, Filomat 38(32) (2024) 11453–11475. [2] H. Azin, F. Mohammadi, M.H. Heydari, A hybrid method for solving time fractional advection diffusion equation on unbounded space domain, Adv. Differ. Equ. 2020 (596) (2020). [3] A. Bhardwaj, A. Kumar, A numerical solution of time-fractional mixed diffusion and diffu sion–wave equation by an RBF-based meshless method, Eng. Comput. 38 (2022) 1883–1903. [4] A.H. Bhrawy, A new numerical algorithm for solving a class of fractional advection–dispersion equation with variable coefficients using Jacobi polynomials, Abstr. Appl. Anal. (2013), Article ID 954983. [5] S. Cao, J. Jiang, J. Wu, Solving time-fractional advection–dispersion equation by variable weights particle tracking method, J. Stat. Phys. 168 (2017) 1248–1258. [6] I. Fahimi-khalilabad, S. Irandoust-pakchin, S.Abdi-mazraeh, High-order finite difference method based on linear barycentric rational interpolation for Caputo type sub-diffusion equation, Math. Comput. Simul. 199 (2022) 60–80 [7] S. Irandoust-pakchin, S. Abdi-mazraeh, A. Khani, Numerical solution for a variable-order frac tional nonlinear cable equation via Chebyshev cardinal functions, Comput. Math. and Math. Phys. 57 (2017) 2047–2056. [8] S. Irandoust-pakchin, S. Abdi-mazraeh, I. Fahimi-khalilabad, Higher order class of finite differ ence method for time-fractional Liouville-Caputo and space-Riesz fractional diffusion equation, Filomat 38(2) (2024) 505–521. [9] S. Irandoust-pakchin, Sh. Babapour, M Lakestani, Image deblurring using adaptive fractional order shock filter, Math. Methods Appl. Sci. 44(6) (2021) 4907–4922. [10] S. Irandoust-Pakchin, M. Lakestani, H. Kheiri, Numerical approach for solving a class of nonlin ear fractional differential equation, Bull. Iran. Math. Soc. 42(5) (2016) 1107–1126. [11] M. Irodotou-Ellina, E.N. Houstis, An O(h6) quintic spline collocation method for fourth order two-point boundary value problems, BIT 28 (1988) 288–301. [12] I. Karatay, N. Kale, S.R. Bayramoglu, A new difference scheme for time fractional heat equations based on the Crank–Nicolson method, Fract. Calc. Appl. Anal. 16(4) (2013) 892–910. [13] M.M.Khader, N.H.Sweilam, Approximate solutions for the fractional advection-dispersion equa tion using Legendre pseudo-spectral method, Comp. Appl. Math. 33 (2014) 739—750. [14] Z. Liu, X. Li, A Crank–Nicolson difference scheme for the time-variable fractional mo bile–immobile advection–dispersion equation, Comput. Appl. Math. 56 (2018) 391–410. [15] C.P. Li, F. Zeng, Numerical Methods for Fractional Calculus, CRC Press, Boca Raton, 2015. [16] C.E. Mej´ ıa, A. Piedrahita, A numerical method for a time-fractional advection–dispersion equa tion with a nonlinear source term, J. Appl. Math. Comput. 61 (2019) 593–609. [17] A.S. Moghadam, M.Arabameri, M.Barfeie, Numerical solution of space–time variable fractional order advection–dispersion equation using radial basis functions, J. Math. Model. 10(3) (2022) 549–562. [18] A. Mohebbi, M. Abbaszadeh, Compact finite difference scheme for the solution of time-fractional advection–dispersion equation, Numer. Algorithms 63(3) (2013) 431–452. [19] S. Momani, Z. Odibat, Numerical solutions of the space–time fractional advection–dispersion equation, Numer. Methods Partial Differ. Equ. 24(6) (2008) 549–562. [20] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Frac tional Differential Equations, to Methods of Their Solution and Some of Their Applications, El seier, 1998. [21] A.S.V. Ravi Kanth, S. Deepika, Application and analysis of spline approximation for time fractional mobile–immobile advection–dispersion equation, Numer. Methods Partial Differ. Equ. 34(5) (2018) 1799–1819 [22] P. Roul, A high accuracy numerical method and its convergence for time-fractional Black-Scholes equation governing European options, Appl. Numer. Math. 151 (2020) 472–493; [23] P. Roul, V.M.K. Prasad Goura, R. Agarwal, A new high order numerical approach for a class of nonlinear derivative dependent singular boundary value problems, Appl. Numer. Math. 145 (2019) 315–341. [24] P. Roul, K. Thula, V.M.K. Prasad Goura, An optimal sixth-order quartic B-spline collocation method for solving Bratu-type and Lane-Emden type problems, Math. Methods Appl. Sci. 42(8) (2019) 2613–2630. [25] V. Saw, S. Kumar, Fourth kind shifted chebyshev polynomials for solving space fractional order advection–dispersion equation, based on collocation method and finite difference approximation, Int. J. Appl. Comput. Math. 4 (2018), Article 82. [26] V. Saw, S. Kumar, Second kind Chebyshev polynomials for solving space-fractional advec tion–dispersion equation using collocation method, Iran. J. Sci. Technol. A Sci. 43 (2019) 1027 1037. [27] M. Shakeel, I. Hussain, H. Ahmad, I. Ahmad, P. Thounthong, Y.F. Zhang, Meshless technique for the solution of time-fractional partial differential equations having real-world applications, J. Funct. Spaces (2020) Article ID 8898309. [28] M.K. Singh, A. Chatterjee, Solution of one-dimensional space- and time-fractional advec tion–dispersion equation by homotopy perturbation method, Acta Geophys. 65(2) (2017) 353 361. [29] M.K. Singh, A. Chatterjee, V.P. Singh, Solution of one-dimensional time-fractional advec tion–dispersion equation by homotopy analysis method, J. Eng. Mech. 143(9) (2017) 1–16. [30] H. Singh, Jacobi collocation method for the fractional advection–dispersion equation arising in porous media, Numer. Methods Partial Differ. Equ. 38(3) (2020) 636–653. [31] K.Thula, P. Roul, A high-order B-spline collocation method for solving nonlinear singular bound ary value problems arising in engineering and applied science, Mediterr. J. Math., 15(176) (2018) | ||
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