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Simulation of Flow in Fractured Poroelastic Media: A Comparison of Different Discretization Approaches Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Efficient Application of the Two-Grid Technique for Solving Time-Fractional Non-linear Parabolic Problem

Author : Miglena N. Koleva

Published in: Finite Difference Methods,Theory and Applications

Publisher: Springer International Publishing

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Abstract

In this paper we present numerical methods for solving a non-linear time-fractional parabolic model. To cope with non-local in time nature of the problem, we exploit the idea of the two-grid method and develop fast numerical algorithms. Moreover, we show that suitable modifications of the standard two-grid technique lead to significant reduction of the computational time. Numerical results are also discussed.

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Literature
1.
2.
Bear, J.: Dynamics of Fluids in Porous Media. American Elsevier, New York (1972)MATH
3.
Cui, M.: Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation. Numer. Algor. 62(3), 383–409 (2013)MATHCrossRef
4.
El-Sayed, A.M.A., Rida, S.Z., Arafa, A.A.M.: Exact solutions of fractional-order biological population model. Commun. Theor. Phys. 52, 992–996 (2009)MathSciNetCrossRef
5.
Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)MATHCrossRef
6.
7.
Ishimura, N., Koleva, M.N., Vulkov, L.G.: Numerical solution via transformation methods of nonlinear models in option pricing. Am. Inst. Phys. CP 1301, 387–394 (2010)
8.
Jiang, X.Y., Xu, M.Y.: Analysis of fractional anomalous diffusion caused by an instantaneous point source in disordered fractal media. Int. J. Nonlinear Mech. 41, 156–165 (2006)CrossRef
9.
Jin, J., Shu, S., Xu, J.: A two-grid discretization method for decoupling systems of partial differential equations. Math. Comput. 75, 1617–1626 (2006)MATHMathSciNetCrossRef
10.
Koçak, H., Yildirim, A.: An efficient new iterative method for finding exact solutions of nonlinear time-fractional partial differential equations. Nonlinear Anal. Model. Control 16(4), 403–414 (2011)MATHMathSciNet
11.
Koleva, M.N., Vulkov, L.G.: A two-grid approximation of an interface problem for the nonlinear Poisson-Boltzmann equation. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds.) NAA 2008. LNCS, vol. 5434, pp. 369–376. Springer, Heidelberg (2009) CrossRef
12.
Koleva, M.N., Vulkov, L.G.: Two-grid quasilinearization approach to ODEs with applications to model problems in physics and mechanics. Comput. Phys. Commun. 181, 663–670 (2010)MATHMathSciNetCrossRef
13.
Liu, Y., Li, Z., Zhang, Y.: Homotopy perturbation method to fractional biological population equation. Fract. Diff. Calc. 1, 117–124 (2011)MathSciNetCrossRef
14.
Lu, Y.G.: Hölder estimates of solutions of biological population equations. Appl. Math. Lett. 13, 123–126 (2000)MATHCrossRef
15.
Metzler, R., Klafter, J.: The random walks guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339, 1–77 (2000)MATHMathSciNetCrossRef
16.
Okubo, A.: Diffusion and Ecological Problem: Mathematical Models. Biomathematics 10. Springer, Berlin (1980)
17.
Patlashenko, I., Givoli, D., Barbone, P.: Time-stepping schemes for systems of Volterra integrodifferential equations. Comput. Methods Appl. Mech. Eng. 190, 5691–5718 (2001)MATHMathSciNetCrossRef
18.
Roul, P.: Application of homotopy perturbation method to biological population model. Appl. Appl. Math. 5(10), 1369–1378 (2010)MATHMathSciNet
19.
Wang, P., Zheng, C., Gorelick, S.: A general approach to advective-dispersive transport with multirate mass transfer. Adv. Water. Res. 28, 33–42 (2005)CrossRef
20.
21.
Metadata
Title
Efficient Application of the Two-Grid Technique for Solving Time-Fractional Non-linear Parabolic Problem
Author
Miglena N. Koleva
Copyright Year
2015
Book
Finite Difference Methods,Theory and Applications

Print ISBN: 978-3-319-20238-9

Electronic ISBN: 978-3-319-20239-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-20239-6_27

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