nach oben

Journal of Applied Mathematics and Computing

Erschienen in:

03.01.2017 | Original Research

A Crank–Nicolson difference scheme for the time variable fractional mobile–immobile advection–dispersion equation

verfasst von: Zhengguang Liu, Xiaoli Li

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

A Crank–Nicolson finite difference scheme to solve a time variable order fractional mobile–immobile advection–dispersion equation is introduced and analyzed. Some a priori estimates of discrete \(L^2\)-norm with order of convergence \(O(\tau +h^2)\) are established on uniform grids where \(\tau \) and h are the steps sizes in time and space. Stability and convergence of the numerical solutions are presented in detail. Numerical examples are provided to verify the theoretical analysis.

Vorheriger Artikel A six-point nonlocal boundary value problem of nonlinear coupled sequential fractional integro-differential equations and coupled integral boundary conditions

Nächster Artikel Two proximal splitting methods for multi-block separable programming with applications to stable principal component pursuit

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Zhang, N., Deng, W., Wu, Y.: Finite difference/element method for a two-dimensional modified fractional diffusion equation. Adv. Appl. Math. Mech. 4(04), 496–518 (2012)MathSciNetCrossRefMATH

Jiang, Y., Ma, J.: High-order finite element methods for time-fractional partial differential equations. J. Comput. Appl. Math. 235(11), 3285–3290 (2011)MathSciNetCrossRefMATH

Li, W., Da, X.: Finite central difference/finite element approximations for parabolic integro-differential equations. Computing 90(3–4), 89–111 (2010)MathSciNetCrossRefMATH

Zeng, F., Li, C., Liu, F., Turner, I.: The use of finite difference/element approaches for solving the time-fractional subdiffusion equation. SIAM J. Sci. Comput. 35(6), A2976–A3000 (2013)MathSciNetCrossRefMATH

Liu, Y., Li, H., Gao, W., He, S., Fang, Z.: A new mixed element method for a class of time-fractional partial differential equations. Sci. World J. 141467 (2014)

Zhao, Y., Chen, P., Bu, W. et al.: Two mixed finite element methods for time-fractional diffusion equations. J. Sci. Comput. 1–22 (2015). doi:10.1007/s10915-015-0152-y

Liu, Y., Fang, Z., Li, H., He, S.: A mixed finite element method for a time-fractional fourth-order partial differential equation. Appl. Math. Comput. 243, 703–717 (2014)MathSciNetCrossRefMATH

Liu, Y., Du, Y., Li, H., et al.: An \(H^1\)-Galerkin mixed finite element method for time fractional reaction–diffusion equation. J. Appl. Math. Comput. 47(1–2), 103–117 (2015)MathSciNetCrossRefMATH

Sousa, E.: A second order explicit finite difference method for the fractional advection diffusion equation. Comput. Math. Appl. 64(10), 3141–3152 (2012)MathSciNetCrossRefMATH

10.

Sousa, E.: An explicit high order method for fractional advection diffusion equations. J. Comput. Phys. 278, 257–274 (2014)MathSciNetCrossRefMATH

11.

Sousa, E.: Finite difference approximations for a fractional advection diffusion problem. J. Comput. Phys. 228(11), 4038–4054 (2009)MathSciNetCrossRefMATH

12.

Huang, J., Tang, Y., Vzquez, L., et al.: Two finite difference schemes for time fractional diffusion-wave equation. Numer. Algorithms 64(4), 707–720 (2013)MathSciNetCrossRefMATH

13.

Li, X., Rui, H.: Characteristic block-centred finite difference methods for nonlinear convection-dominated diffusion equation. Int. J. Comput. Math. 1–19 (2015). doi:10.1080/00207160.2015.1109641

14.

Li, X., Rui, H.: A two-grid block-centered finite difference method for nonlinear non-fickian flow model. Appl. Math. Comput. 281, 300–313 (2016)MathSciNetCrossRef

15.

Liu, Z., Li, X.: A parallel CGS block-centered finite difference method for a nonlinear time-fractional parabolic equation. Comput. Methods Appl. Mech. Eng. 308, 330–348 (2016)MathSciNetCrossRef

16.

Cheng, A., Wang, H., Wang, K.: A Eulerian–Lagrangian control volume method for solute transport with anomalous diffusion. Numer. Methods Partial Differ. Eqs. 31(1), 253–267 (2015)MathSciNetCrossRefMATH

17.

Liu, F., Zhuang, P., Turner, I., et al.: A new fractional finite volume method for solving the fractional diffusion equation. Appl. Math. Model. 38(15), 3871–3878 (2014)MathSciNetCrossRef

18.

Wei, L., He, Y.: Analysis of a fully discrete local discontinuous Galerkin method for time-fractional fourth-order problems. Appl. Math. Model. 38(4), 1511–1522 (2014)MathSciNetCrossRef

19.

Liu, X., et al.: On some new integral inequalities of Gronwall–Bellman–Bihari type with delay for discontinuous functions and their applications. Indag. Math. 27, 1–10 (2016)MathSciNetCrossRefMATH

20.

Lin, Y., Xu, C.: Finite difference/spectral approximations for the time-fractional diffusion equation. J. Comput. Phys. 225(2), 1533–1552 (2007)MathSciNetCrossRefMATH

21.

Lin, Y., Li, X., Xu, C.: Finite difference/spectral approximations for the fractional cable equation. Math. Comput. 80(275), 1369–1396 (2011)MathSciNetCrossRefMATH

22.

Zhao, X., Sun, Z., Karniadakis, G.E.: Second-order approximations for variable order fractional derivatives: algorithms and applications. J. Comput. Phys. 293, 184–200 (2015)MathSciNetCrossRefMATH

23.

Zhang, H., Liu, F., Phanikumar, M.S., Meerschaert, M.M.: A novel numerical method for the time variable fractional order mobile–immobile advection–dispersion model. Comput. Math. Appl. 66(5), 693–701 (2013)MathSciNetCrossRefMATH

24.

Atangana, A.: On the stability and convergence of the time-fractional variable order telegraph equation. J. Comput. Phys. 293, 104–114 (2015)MathSciNetCrossRefMATH

25.

Atangana, A., Baleanu, D.: Numerical solution of a kind of fractional parabolic equations via two difference schemes. Abstr. Appl. Anal. 141467 (2013)

26.

Zhang, Y., Benson, D.A., Reeves, D.M.: Time and space nonlocalities underlying fractional-derivative models: distinction and literature review of field applications. Adv. Water Resour. 32(4), 561–581 (2009)CrossRef

27.

Schumer, R., Benson, D.A., Meerschaert, M.M., Baeumer, B.: Fractal mobile/immobile solute transport. Water Resour. Res. 39(10) (2003). doi:10.1029/2003WR002141

28.

Liu, Qingxia, et al.: A RBF meshless approach for modeling a fractal mobile/immobile transport model. Appl. Math. Comput. 226, 336–347 (2014)MathSciNetCrossRefMATH

29.

Liu, F., Zhuang, P., Burrage, K.: Numerical methods and analysis for a class of fractional advection–dispersion models. Comput. Math. Appl. 64(10), 2990–3007 (2012)MathSciNetCrossRefMATH

30.

Ashyralyev, A., Cakir, Z.: On the numerical solution of fractional parabolic partial differential equations with the Dirichlet condition. Discret. Dyn. Nat. Soc. (2012). doi:10.1155/2012/696179

31.

Ashyralyev, A., Cakir, Z.: Fdm for fractional parabolic equations with the Neumann condition. Adv. Differ. Eqs. 2013(1), 1–16 (2013)CrossRefMATH

32.

Karatay, I., Kale, N., Bayramoglu, S.R.: A new difference scheme for time fractional heat equations based on the Crank–Nicholson method. Fract. Calc. Appl. Anal. 16(4), 892–910 (2014)MATH

Titel: A Crank–Nicolson difference scheme for the time variable fractional mobile–immobile advection–dispersion equation
verfasst von: Zhengguang Liu
Xiaoli Li
Publikationsdatum: 03.01.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2018
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-016-1079-7

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1-2/2018

Existence results for BVP of a class of Hilfer fractional differential equations

A mathematical study of an imprecise SIR epidemic model with treatment control

Well-defined solutions of a system of difference equations

Transformation techniques and positive solutions on a parameter for three-point impulsive differential equations

Stochastic permanence of two impulsive stochastic delay single species systems incorporating predation term

Analyzing on stability of HIV-PI model with general incidence rate