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Volumn 16, Issue 6, 2011, Pages 2535-2542

On the numerical solutions for the fractional diffusion equation

Author keywords

Caputo derivative; Chebyshev polynomials; Finite difference method; Fractional diffusion equation

Indexed keywords

DIFFUSION; FINITE DIFFERENCE METHOD; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS;

EID: 78651444144     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.09.007     Document Type: Article
Times cited : (250)

References (16)
  • 1
    • 0021439912 scopus 로고
    • On the appearance of the fractional derivative in the behavior of real materials
    • Bagley R.L., Torvik P.J. On the appearance of the fractional derivative in the behavior of real materials. J Appl Mech 1984, 51:294-298.
    • (1984) J Appl Mech , vol.51 , pp. 294-298
    • Bagley, R.L.1    Torvik, P.J.2
  • 3
    • 0001618393 scopus 로고    scopus 로고
    • An algorithm for the numerical solution of differential equations of fractional order
    • Diethelm K. An algorithm for the numerical solution of differential equations of fractional order. Electron Trans Numer Anal 1997, 5:1-6.
    • (1997) Electron Trans Numer Anal , vol.5 , pp. 1-6
    • Diethelm, K.1
  • 5
    • 0032307661 scopus 로고    scopus 로고
    • Approximate analytical solution for seepage flow with fractional derivatives in porous media
    • He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput Meth Appl Mech Eng 1998, 167(1-2):57-68.
    • (1998) Comput Meth Appl Mech Eng , vol.167 , Issue.1-2 , pp. 57-68
    • He, J.H.1
  • 6
    • 43949121726 scopus 로고    scopus 로고
    • The approximate and exact solutions of the space- and time-fractional Burger's equations with initial conditions by variational iteration method
    • Inc M. The approximate and exact solutions of the space- and time-fractional Burger's equations with initial conditions by variational iteration method. J Math Anal Appl 2008, 345:476-484.
    • (2008) J Math Anal Appl , vol.345 , pp. 476-484
    • Inc, M.1
  • 7
    • 33748959199 scopus 로고    scopus 로고
    • Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition
    • Jafari H., Daftardar-Gejji V. Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition. Appl Math Comput 2006, 180:488-497.
    • (2006) Appl Math Comput , vol.180 , pp. 488-497
    • Jafari, H.1    Daftardar-Gejji, V.2
  • 8
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • Lubich Ch. Discretized fractional calculus. SIAM J Math Anal 1986, 17:704-719.
    • (1986) SIAM J Math Anal , vol.17 , pp. 704-719
    • Lubich, C.1
  • 9
    • 4444368867 scopus 로고    scopus 로고
    • Finite difference approximations for fractional advection-dispersion flow equations
    • Meerschaert M.M., Tadjeran C. Finite difference approximations for fractional advection-dispersion flow equations. J Comput Appl Math 2004, 172(1):65-77.
    • (2004) J Comput Appl Math , vol.172 , Issue.1 , pp. 65-77
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 10
    • 28044468843 scopus 로고    scopus 로고
    • Finite difference approximations for two-sided space-fractional partial differential equations
    • Meerschaert M.M., Tadjeran C. Finite difference approximations for two-sided space-fractional partial differential equations. Appl Numer Math 2006, 56:80-90.
    • (2006) Appl Numer Math , vol.56 , pp. 80-90
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 12
    • 33646161468 scopus 로고    scopus 로고
    • Numerical solution of fractional integro-differential equations by collocation method
    • Rawashdeh E.A. Numerical solution of fractional integro-differential equations by collocation method. Appl Math Comput 2006, 176:1-6.
    • (2006) Appl Math Comput , vol.176 , pp. 1-6
    • Rawashdeh, E.A.1
  • 15
    • 35349007940 scopus 로고    scopus 로고
    • Numerical studies for a multi-order fractional differential equation
    • Sweilam N.H., Khader M.M., Al-Bar R.F. Numerical studies for a multi-order fractional differential equation. Phys Lett A 2007, 371:26-33.
    • (2007) Phys Lett A , vol.371 , pp. 26-33
    • Sweilam, N.H.1    Khader, M.M.2    Al-Bar, R.F.3
  • 16
    • 33845628108 scopus 로고    scopus 로고
    • A second-order accurate numerical method for the two dimensional fractional diffusion equation
    • Tadjeran C., Meerschaert M.M. A second-order accurate numerical method for the two dimensional fractional diffusion equation. J Comput Phys 2007, 220:813-823.
    • (2007) J Comput Phys , vol.220 , pp. 813-823
    • Tadjeran, C.1    Meerschaert, M.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.