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Volumn 10, Issue 1, 2012, Pages 1-8

Anomalous sub-diffusion equations by the meshless collocation method

Author keywords

Anomalous sub diffusion equation; Collocation scheme; Fractional differential equation; Meshless method; Moving least squares

Indexed keywords

ANOMALOUS SUB-DIFFUSION EQUATION; COLLOCATION SCHEME; FRACTIONAL DIFFERENTIAL EQUATIONS; MESH-LESS METHODS; MOVING LEAST SQUARES;

EID: 84869392671     PISSN: 14484846     EISSN: None     Source Type: Journal    
DOI: 10.7158/M10-722.2012.10.1     Document Type: Article
Times cited : (13)

References (26)
  • 2
    • 0032136132 scopus 로고    scopus 로고
    • A new meshfree local Petrov-Galerkin (MLPG) approach in computational
    • Atluri, S. N. & Zhu, T. 1998, "A new meshfree local Petrov-Galerkin (MLPG) approach in computational mechanics", Computational Mechanics, Vol. 22, pp. 117-127.
    • (1998) Mechanics, Computational Mechanics , vol.22 , pp. 117-127
    • Atluri, S.N.1    Zhu, T.2
  • 4
    • 0034032484 scopus 로고    scopus 로고
    • Application of a fractional advection dispertion equation
    • Benson, D. A., Wheatcraft, S. W., & Meerschaert, M. M. 2000, "Application of a fractional advection dispertion equation", Water Resour. Res., Vol. 36, No. 6, pp. 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
  • 6
    • 76449113714 scopus 로고    scopus 로고
    • Fractional diffusion equations by the Kansa method
    • Chen, W., Ye, L. & Sun, H. 2010, "Fractional diffusion equations by the Kansa method", Computers and Mathematics with Applications, Vol. 59, No. 5, pp. 1614-1620.
    • (2010) Computers and Mathematics With Applications , vol.59 , Issue.5 , pp. 1614-1620
    • Chen, W.1    Ye, L.2    Sun, H.3
  • 7
    • 85183430449 scopus 로고
    • Smooth particle hydrodynamics: Theory and applications to non-spherical stars
    • Gingold, R. A. & Moraghan, J. J. 1977, "Smooth particle hydrodynamics: theory and applications to non-spherical stars", Monthly Notices of the Royal Astronomical Society, Vol. 181, 375-389.
    • (1977) Monthly Notices of the Royal Astronomical Society , vol.181 , pp. 375-389
    • Gingold, R.A.1    Moraghan, J.J.2
  • 8
    • 33846288234 scopus 로고    scopus 로고
    • Meshfree methods and their comparisons
    • Gu, Y. T. 2005, "Meshfree methods and their comparisons", International Journal of Computational Methods, Vol. 2, No. 4, pp. 477-515.
    • (2005) International Journal of Computational Methods , vol.2 , Issue.4 , pp. 477-515
    • Gu, Y.T.1
  • 9
    • 0035261976 scopus 로고    scopus 로고
    • A boundary point interpolation method for stress analysis of solids
    • Gu, Y. T. & Liu, G. R. 2002, "A boundary point interpolation method for stress analysis of solids", Computational Mechanics, Vol. 28, pp. 47-54.
    • (2002) Computational Mechanics , vol.28 , pp. 47-54
    • Gu, Y.T.1    Liu, G.R.2
  • 10
    • 0037407334 scopus 로고    scopus 로고
    • A boundary radial point interpolation method (BRPIM) for 2-D structural analyses
    • Gu, Y. T. & Liu, G. R. 2003, "A boundary radial point interpolation method (BRPIM) for 2-D structural analyses", Structural Engineering and Mechanics, Vol. 15, No. 5, pp. 535-550.
    • (2003) Structural Engineering and Mechanics , vol.15 , Issue.5 , pp. 535-550
    • Gu, Y.T.1    Liu, G.R.2
  • 11
    • 77951184169 scopus 로고    scopus 로고
    • An Advanced Implicit Meshless Approach for the Non-linear Anomalous Subdiffusion Equation
    • Gu, Y. T., Zhuang, P. & Liu, F. 2010, "An Advanced Implicit Meshless Approach for the Non-linear Anomalous Subdiffusion Equation", CMES, Vol. 56, No. 3, pp. 303-333.
    • (2010) CMES , vol.56 , Issue.3 , pp. 303-333
    • Gu, Y.T.1    Zhuang, P.2    Liu, F.3
  • 12
    • 0025229330 scopus 로고
    • Multiquadrics A Scattered Data Approximation Scheme with Applications to Computational Fluid dynamics
    • Kansa, E. J. 1990, "Multiquadrics A Scattered Data Approximation Scheme with Applications to Computational Fluid dynamics", Computers Math. Applic., Vol. 19, No. 8/9, pp. 127-145.
    • (1990) Computers Math. Applic , vol.19 , Issue.8-9 , pp. 127-145
    • Kansa, E.J.1
  • 13
    • 0035817769 scopus 로고    scopus 로고
    • A local radial point interpolation method (LR-PIM) for free vibration analyses of 2-D solids
    • Liu, G. R. & Gu, Y. T. 2001a, "A local radial point interpolation method (LR-PIM) for free vibration analyses of 2-D solids", Journal of Sound and Vibration, Vol. 246, No. 1, pp. 29-46.
    • (2001) Journal of Sound and Vibration , vol.246 , Issue.1 , pp. 29-46
    • Liu, G.R.1    Gu, Y.T.2
  • 16
    • 1542749194 scopus 로고    scopus 로고
    • Assessment and applications of point interpolation methods for computational mechanics
    • Liu, G. R., Gu, Y. T. & Dai, K. Y. 2004, "Assessment and applications of point interpolation methods for computational mechanics", Int. J. for Numerical Methods in Eng., Vol. 59, No. 10, pp. 1373-1397.
    • (2004) Int. J. For Numerical Methods In Eng , vol.59 , Issue.10 , pp. 1373-1397
    • Liu, G.R.1    Gu, Y.T.2    Dai, K.Y.3
  • 18
    • 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. & Burrage, K. 2007, "Stability and convergence of the difference methods for the space-time fractional advection diffusion equation", Applied Mathematics and Computation, Vol. 191, pp. 12-20.
    • (2007) Applied Mathematics and Computation , vol.191 , pp. 12-20
    • Liu, F.1    Zhuang, P.2    Anh, V.3    Turner, I.4    Burrage, K.5
  • 19
    • 4444368867 scopus 로고    scopus 로고
    • Finite difference approximations for fractional advection dispersion flow equations
    • Meerschaert, M. & Tadjeran, C. 2004, "Finite difference approximations for fractional advection dispersion flow equations", J. Comput. Appl. Math., Vol. 172, pp. 65-77.
    • (2004) J. Comput. Appl. Math , vol.172 , pp. 65-77
    • Meerschaert, M.1    Tadjeran, C.2
  • 21
    • 0027035536 scopus 로고
    • Generalizing the finite element method: Diffuse approximation and diffuse elements
    • Nayroles, B., Touzot, G. & Villon, P. 1992, "Generalizing the finite element method: diffuse approximation and diffuse elements", Computational Mechanics, Vol. 10, pp. 307-318.
    • (1992) Computational Mechanics , vol.10 , pp. 307-318
    • Nayroles, B.1    Touzot, G.2    Villon, P.3
  • 23
    • 0031983021 scopus 로고    scopus 로고
    • Structural mosaicism on the submicron scale in the plasma membrane
    • Simson, R., Yang, B., Moore, S., Doherty, P., Walsh, F. & Jacobson, K. 1998, "Structural mosaicism on the submicron scale in the plasma membrane", Biophys. J., Vol. 74, pp. 297-308.
    • (1998) Biophys. J , vol.74 , pp. 297-308
    • Simson, R.1    Yang, B.2    Moore, S.3    Doherty, P.4    Walsh, F.5    Jacobson, K.6
  • 24
    • 31144434675 scopus 로고    scopus 로고
    • From diffusion to anomalous diffusion: A century after Einstein's Brownian motion
    • Sokolov, I. & Klafter, J. 2005, "From diffusion to anomalous diffusion: a century after Einstein's Brownian motion", Chaos, Vol. 15.
    • (2005) Chaos , pp. 15
    • Sokolov, I.1    Klafter, J.2
  • 25
    • 0032048673 scopus 로고    scopus 로고
    • A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method
    • Zhu, T. & Atluri, S. N. 1998, "A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method", Computational Mechanics, Vol. 21, pp. 211-222.
    • (1998) Computational Mechanics , vol.21 , pp. 211-222
    • Zhu, T.1    Atluri, S.N.2
  • 26
    • 55549107511 scopus 로고    scopus 로고
    • New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation
    • Zhuang, P., Liu, F., Anh, V. & Turner, I. 2008, "New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation", SIAM Journal on Numerical Analysis, Vol. 46, No. 2, pp. 1079-1095.
    • (2008) SIAM Journal On Numerical Analysis , vol.46 , Issue.2 , pp. 1079-1095
    • Zhuang, P.1    Liu, F.2    Anh, V.3    Turner, I.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.