메뉴 건너뛰기




Volumn 216, Issue 8, 2010, Pages 2248-2262

Analytical and numerical solutions of a one-dimensional fractional-in-space diffusion equation in a composite medium

Author keywords

Composite medium; Fractional diffusion; Global eigenfunction expansion; Global scheme; Numerical approximation

Indexed keywords

ANALYTICAL AND NUMERICAL SOLUTIONS; COMPOSITE MEDIUM; DIFFUSION EQUATIONS; DOMAIN DECOMPOSITIONS; EIGENFUNCTION EXPANSIONS; FRACTIONAL DIFFUSION; FRACTIONAL DIFFUSION EQUATION; FRACTIONAL EXPONENT; GLOBAL SOLUTIONS; LINEAR ODES; MATRIX; MATRIX REPRESENTATION; NEUMANN CONDITION; NUMERICAL APPROXIMATIONS; NUMERICAL SOLUTION; NUMERICAL STRATEGIES; SIMULATION RESULT; SPACE OPERATORS; TWO LAYERS;

EID: 77953127197     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.03.060     Document Type: Article
Times cited : (23)

References (46)
  • 1
    • 0035538580 scopus 로고    scopus 로고
    • Spectral analysis of fractional kinetic equations with random data
    • Anh V.V., and Leonenko N.N. Spectral analysis of fractional kinetic equations with random data. J. Stat. Phys. 104 (2001) 349-1387
    • (2001) J. Stat. Phys. , vol.104 , pp. 349-1387
    • Anh, V.V.1    Leonenko, N.N.2
  • 2
    • 0036026997 scopus 로고    scopus 로고
    • Renormalization and homogenization of fractional diffusion equations with random data
    • Anh V.V., and Leonenko N.N. Renormalization and homogenization of fractional diffusion equations with random data. Probab. Theor. Relat. Field 12 (2002) 381-408
    • (2002) Probab. Theor. Relat. Field , vol.12 , pp. 381-408
    • Anh, V.V.1    Leonenko, N.N.2
  • 3
    • 0039302360 scopus 로고    scopus 로고
    • Multifractal characterisation of complete genomes
    • Anh V.V., Lau K.S., and Yu Z.G. Multifractal characterisation of complete genomes. J. Phys. A: Math. Gen. 34 (2001) 7127-7139
    • (2001) J. Phys. A: Math. Gen. , vol.34 , pp. 7127-7139
    • Anh, V.V.1    Lau, K.S.2    Yu, Z.G.3
  • 5
    • 34250095360 scopus 로고
    • Uniqueness in law for pure jump type Markov processes
    • Bass R.F. Uniqueness in law for pure jump type Markov processes. Probab. Theor. Relat. Field 79 (1988) 271-287
    • (1988) Probab. Theor. Relat. Field , vol.79 , pp. 271-287
    • Bass, R.F.1
  • 7
    • 0034032484 scopus 로고    scopus 로고
    • Application of a fractional advection-dispersion equation
    • Benson D.A., Wheatcraft S.W., and Meerschaert M.M. Application of a fractional advection-dispersion equation. Water Resour. Res. 36 6 (2000) 1403-1412
    • (2000) Water Resour. Res. , vol.36 , Issue.6 , pp. 1403-1412
    • Benson, D.A.1    Wheatcraft, S.W.2    Meerschaert, M.M.3
  • 8
    • 0034113992 scopus 로고    scopus 로고
    • The fractional-order governing equation of Levy motion
    • Benson D.A., Wheatcraft S.W., and Meerschaert M.M. The fractional-order governing equation of Levy motion. Water Resour. Res. 36 6 (2000) 1413-1423
    • (2000) Water Resour. Res. , vol.36 , Issue.6 , pp. 1413-1423
    • Benson, D.A.1    Wheatcraft, S.W.2    Meerschaert, M.M.3
  • 12
    • 0004185784 scopus 로고
    • Cambridge University Press
    • Frisch U. Turbulence (1995), Cambridge University Press
    • (1995) Turbulence
    • Frisch, U.1
  • 13
    • 0000361678 scopus 로고    scopus 로고
    • Random walk models for space fractional diffusion processes
    • Gorenflo R., and Mainardi F. Random walk models for space fractional diffusion processes. Fract. Calc. Appl. Anal. 1 (1998) 167-191
    • (1998) Fract. Calc. Appl. Anal. , vol.1 , pp. 167-191
    • Gorenflo, R.1    Mainardi, F.2
  • 14
    • 0027456173 scopus 로고
    • A statistical analysis of mesoscale rainfall as a random cascade
    • Gupta V.K., and Waymire E.C. A statistical analysis of mesoscale rainfall as a random cascade. J. Appl. Meteorol. 32 (1993) 251-267
    • (1993) J. Appl. Meteorol. , vol.32 , pp. 251-267
    • Gupta, V.K.1    Waymire, E.C.2
  • 16
    • 64249135201 scopus 로고    scopus 로고
    • Numerical approximation of a fractional-in-space diffusion equation
    • Ilic M., Liu F., Turner I., and Anh V. Numerical approximation of a fractional-in-space diffusion equation. Fract. Calc. Appl. Anal. 8 3 (2005) 323-341
    • (2005) Fract. Calc. Appl. Anal. , vol.8 , Issue.3 , pp. 323-341
    • Ilic, M.1    Liu, F.2    Turner, I.3    Anh, V.4
  • 17
    • 64249104309 scopus 로고    scopus 로고
    • Numerical approximation of a fractional-in-space diffusion equation (II)-with nonhomogeneous boundary conditions
    • Ilic M., Liu F., Turner I., and Anh V. Numerical approximation of a fractional-in-space diffusion equation (II)-with nonhomogeneous boundary conditions. Fract. Calc. Appl. Anal. 9 4 (2006) 333-349
    • (2006) Fract. Calc. Appl. Anal. , vol.9 , Issue.4 , pp. 333-349
    • Ilic, M.1    Liu, F.2    Turner, I.3    Anh, V.4
  • 18
    • 51249166005 scopus 로고
    • A class of Feller semigroups generated by pseudodifferential operators
    • Jacob N. A class of Feller semigroups generated by pseudodifferential operators. Math. Z. 215 (1994) 151-166
    • (1994) Math. Z. , vol.215 , pp. 151-166
    • Jacob, N.1
  • 19
    • 0013118687 scopus 로고
    • Pseudodifferential operators with variable order of differentiation generating Feller semigroup
    • Jacob N., and Leopold H.G. Pseudodifferential operators with variable order of differentiation generating Feller semigroup. Integr. Eq. Oper. Theor. 17 (1993) 544-553
    • (1993) Integr. Eq. Oper. Theor. , vol.17 , pp. 544-553
    • Jacob, N.1    Leopold, H.G.2
  • 20
    • 0033443957 scopus 로고    scopus 로고
    • The multifractal nature of Lévy processes
    • Jaffard S. The multifractal nature of Lévy processes. Probab. Theor. Relat. Field 114 (1999) 207-227
    • (1999) Probab. Theor. Relat. Field , vol.114 , pp. 207-227
    • Jaffard, S.1
  • 21
    • 0003329153 scopus 로고
    • Sur sertaines martingales de Benoit Mandelbrot
    • Kahane J.P., and Peyrière J. Sur sertaines martingales de Benoit Mandelbrot. Adv. Math. 22 (1976) 131-145
    • (1976) Adv. Math. , vol.22 , pp. 131-145
    • Kahane, J.P.1    Peyrière, J.2
  • 22
    • 0013161462 scopus 로고    scopus 로고
    • On Markov processes generated by pseudodifferentail operator of variable order
    • Kikuchi K., and Negoro A. On Markov processes generated by pseudodifferentail operator of variable order. Osaka J. Math. 34 (1997) 319-335
    • (1997) Osaka J. Math. , vol.34 , pp. 319-335
    • Kikuchi, K.1    Negoro, A.2
  • 24
    • 77953132734 scopus 로고    scopus 로고
    • A finite volume simulation model for saturated-unsaturated flow and application to Gooburrum, Bundaberg, Queensland, Australia
    • Liu F., Anh V., Turner I., Bajracharya K., Huxley W., and Su N. A finite volume simulation model for saturated-unsaturated flow and application to Gooburrum, Bundaberg, Queensland, Australia. Appl. Math. Model. 29 (2005) 852-870
    • (2005) Appl. Math. Model. , vol.29 , pp. 852-870
    • Liu, F.1    Anh, V.2    Turner, I.3    Bajracharya, K.4    Huxley, W.5    Su, N.6
  • 25
    • 1542425102 scopus 로고    scopus 로고
    • Numerical solution of the space fractional Fokker-Planck equation
    • Liu F., Anh V., and Turner I. Numerical solution of the space fractional Fokker-Planck equation. J. Comput. Appl. Math. 166 (2004) 209-219
    • (2004) J. Comput. Appl. Math. , vol.166 , pp. 209-219
    • Liu, F.1    Anh, V.2    Turner, I.3
  • 26
    • 33751548431 scopus 로고    scopus 로고
    • Numerical simulation for solute transport in fractal porous media
    • Liu F., Anh V., Turner I., and Zhuang P. Numerical simulation for solute transport in fractal porous media. ANZIAM J. 45 (2004) 461-473
    • (2004) ANZIAM J. , vol.45 , pp. 461-473
    • Liu, F.1    Anh, V.2    Turner, I.3    Zhuang, P.4
  • 27
    • 34547673244 scopus 로고    scopus 로고
    • Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
    • Liu F., Zhuang P., Anh V., Turner I., and Burrage K. Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation. Appl. Math. Comput. 191 (2007) 12-20
    • (2007) Appl. Math. Comput. , vol.191 , pp. 12-20
    • Liu, F.1    Zhuang, P.2    Anh, V.3    Turner, I.4    Burrage, K.5
  • 28
    • 33846798041 scopus 로고    scopus 로고
    • Approximation of the Levy-Feller advection-dispersion process by random walk and finite difference method
    • Liu Q., Liu F., Turner I., and Anh V. Approximation of the Levy-Feller advection-dispersion process by random walk and finite difference method. J. Phys. Comput. 222 (2007) 57-70
    • (2007) J. Phys. Comput. , vol.222 , pp. 57-70
    • Liu, Q.1    Liu, F.2    Turner, I.3    Anh, V.4
  • 29
    • 0001407424 scopus 로고    scopus 로고
    • The fundanental solution of the space-time fractional diffusion equation
    • Mainardi F., Luchko Yu., and Pagnini G. The fundanental solution of the space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 4 2 (2001) 153-192
    • (2001) Fract. Calc. Appl. Anal. , vol.4 , Issue.2 , pp. 153-192
    • Mainardi, F.1    Luchko, Yu.2    Pagnini, G.3
  • 30
    • 0015969022 scopus 로고
    • Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier
    • Mandelbrot B. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62 (1974) 331-358
    • (1974) J. Fluid Mech. , vol.62 , pp. 331-358
    • Mandelbrot, B.1
  • 32
    • 4444368867 scopus 로고    scopus 로고
    • Finite difference approximations for fractional advection-dispersion flow equations
    • Meerschaert M., and Tadjeran C. Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math. 172 (2004) 65-77
    • (2004) J. Comput. Appl. Math. , vol.172 , pp. 65-77
    • Meerschaert, M.1    Tadjeran, C.2
  • 33
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamic approach
    • R. Metzler, J. Krafter, The random walk's guide to anomalous diffusion: a fractional dynamic approach, Phys. Rep. 339 (2000) 1-72.
    • (2000) Phys. Rep , vol.339 , pp. 1-72
    • Metzler, R.1    Krafter, J.2
  • 34
    • 4043151477 scopus 로고    scopus 로고
    • The restaurant at the end of the random walk: recent development in the description of anomalous transport by fractional dynamics
    • Metzler R., and Krafter J. The restaurant at the end of the random walk: recent development in the description of anomalous transport by fractional dynamics. J. Phys. A: Math. Gen. 37 (2004) R161-R208
    • (2004) J. Phys. A: Math. Gen. , vol.37
    • Metzler, R.1    Krafter, J.2
  • 40
    • 0346517294 scopus 로고    scopus 로고
    • Multifractal processes
    • Doukhan P., Oppenheim, and Taqqu M. (Eds), Birkhauser
    • Riedi R.H. Multifractal processes. In: Doukhan P., Oppenheim, and Taqqu M. (Eds). Long Range Dependence: Theory and Applications (2003), Birkhauser 625-716
    • (2003) Long Range Dependence: Theory and Applications , pp. 625-716
    • Riedi, R.H.1
  • 45
    • 70549107817 scopus 로고    scopus 로고
    • Error analysis of an explicit finite difference approximation for the space fractional diffusion
    • Shen S., and Liu F. Error analysis of an explicit finite difference approximation for the space fractional diffusion. ANZIAM J. 46 (2005) 871-887
    • (2005) ANZIAM J. , vol.46 , pp. 871-887
    • Shen, S.1    Liu, F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.