메뉴 건너뛰기




Volumn 66, Issue 5, 2013, Pages 693-701

A novel numerical method for the time variable fractional order mobile-immobile advection-dispersion model

Author keywords

Coimbra variable fractional order derivative; Implicit finite difference method; Mobile immobile advection dispersion equation; Stability and convergence

Indexed keywords

ADVECTION-DISPERSION EQUATION; COMPUTATIONALLY EFFICIENT; FRACTIONAL ORDER DERIVATIVES; IMPLICIT DIFFERENCE APPROXIMATIONS; IMPLICIT FINITE DIFFERENCE METHOD; IMPLICIT NUMERICAL METHOD; NOVEL NUMERICAL METHODS; STABILITY AND CONVERGENCE;

EID: 84881478398     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2013.01.031     Document Type: Article
Times cited : (174)

References (32)
  • 2
  • 3
    • 84874913467 scopus 로고    scopus 로고
    • Application of homotopy perturbation and variational iteration methods for fredholm integrodifferential equation of fractional order
    • 10.1155/2012/763139
    • Asma Ali Elbeleze, Adem Kilicman, and Bachok M. Taib Application of homotopy perturbation and variational iteration methods for fredholm integrodifferential equation of fractional order Abstract and Applied Analysis 2012 76139 10.1155/2012/763139
    • (2012) Abstract and Applied Analysis , pp. 76139
    • Elbeleze, A.A.1    Kilicman, A.2    Taib, B.M.3
  • 4
    • 84861715300 scopus 로고    scopus 로고
    • Solutions of the fractional Davey-Stewartson equations with variational iteration method
    • Hossain Jafari, Abdelouahab Kadem, Dumitru Baleanu, and Tugba Yilmaz Solutions of the fractional Davey-Stewartson equations with variational iteration method Romanian Reports in Physics 64 2 2012 337 346
    • (2012) Romanian Reports in Physics , vol.64 , Issue.2 , pp. 337-346
    • Jafari, H.1    Kadem, A.2    Baleanu, D.3    Yilmaz, T.4
  • 5
    • 31444435831 scopus 로고    scopus 로고
    • Generalized ficks law and fractional ADE for pollutant transport in a river: Detailed derivation
    • S. Kim, and M.L. Kavvas Generalized ficks law and fractional ADE for pollutant transport in a river: detailed derivation Journal of Hydrologic Engineering 11 1 2006 80 83
    • (2006) Journal of Hydrologic Engineering , vol.11 , Issue.1 , pp. 80-83
    • Kim, S.1    Kavvas, M.L.2
  • 6
    • 84860318089 scopus 로고    scopus 로고
    • Solute transport in solution conduits exhibiting multi-peaked breakthrough curves
    • M.S. Field, and F.J. Leij Solute transport in solution conduits exhibiting multi-peaked breakthrough curves Journal of Hydrology 440-441 2012 26 35
    • (2012) Journal of Hydrology , vol.440-441 , pp. 26-35
    • Field, M.S.1    Leij, F.J.2
  • 7
    • 80052779810 scopus 로고    scopus 로고
    • Surface storage dynamics in large rivers: Comparing three-dimensional particle transport, one-dimensional fractional derivative and multi-rate transient storage models
    • 10.1029/2010WR010228
    • E.J. Anderson, and M.S. Phanikumar Surface storage dynamics in large rivers: comparing three-dimensional particle transport, one-dimensional fractional derivative and multi-rate transient storage models Water Resources Research 47 9 2011 W09511 10.1029/2010WR010228
    • (2011) Water Resources Research , vol.47 , Issue.9 , pp. 09511
    • Anderson, E.J.1    Phanikumar, M.S.2
  • 9
    • 34547673244 scopus 로고    scopus 로고
    • Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
    • F. Liu, P. Zhuang, V. Anh, I. Turner, and K. Burrage Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation Applied Mathematics and Computation 191 2007 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
  • 10
    • 79951851714 scopus 로고    scopus 로고
    • Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation
    • S. Shen, F. Liu, and V. Anh Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation Numerical Algorithms 56 3 2011 383 404
    • (2011) Numerical Algorithms , vol.56 , Issue.3 , pp. 383-404
    • Shen, S.1    Liu, F.2    Anh, V.3
  • 11
    • 84868214613 scopus 로고    scopus 로고
    • Numerical methods and analysis for a class of fractional advection-dispersion models
    • F. Liu, P. Zhuang, and K. Burrage Numerical methods and analysis for a class of fractional advection-dispersion models Computers & Mathematics with Applications 64 10 2012 2990 3007
    • (2012) Computers & Mathematics with Applications , vol.64 , Issue.10 , pp. 2990-3007
    • Liu, F.1    Zhuang, P.2    Burrage, K.3
  • 12
    • 0346897985 scopus 로고    scopus 로고
    • Mechanica with variable-order differential operators
    • C.F.M. Coimbra Mechanica with variable-order differential operators Annalen der Physik 12 11-12 2003 692 703
    • (2003) Annalen der Physik , vol.12 , Issue.1112 , pp. 692-703
    • Coimbra, C.F.M.1
  • 13
    • 2942565724 scopus 로고    scopus 로고
    • Filtering using variable order vertical derivatives
    • G.R.J. Cooper, and D.R. Cowan Filtering using variable order vertical derivatives Computers and Geosciences 30 2004 455 459
    • (2004) Computers and Geosciences , vol.30 , pp. 455-459
    • Cooper, G.R.J.1    Cowan, D.R.2
  • 14
    • 33745698055 scopus 로고    scopus 로고
    • Design of variable and adaptive fractional order FIR differentiators
    • C.C. Tseng Design of variable and adaptive fractional order FIR differentiators Signal Processing 86 2006 2554 2566
    • (2006) Signal Processing , vol.86 , pp. 2554-2566
    • Tseng, C.C.1
  • 15
    • 68649098514 scopus 로고    scopus 로고
    • Variable-order fractional differential operators in anomalous diffusion modeling
    • H. Sun, W. Chen, and Y. Chen Variable-order fractional differential operators in anomalous diffusion modeling Physica A 388 2009 4586 4592
    • (2009) Physica A , vol.388 , pp. 4586-4592
    • Sun, H.1    Chen, W.2    Chen, Y.3
  • 16
    • 84948882036 scopus 로고
    • Intergation and differentiation to a variable fractional order
    • S.G. Samko, and B. Ross Intergation and differentiation to a variable fractional order Integral Transforms and Special Functions 1 4 1993 277 300
    • (1993) Integral Transforms and Special Functions , vol.1 , Issue.4 , pp. 277-300
    • Samko, S.G.1    Ross, B.2
  • 18
    • 0010073424 scopus 로고
    • Fractional integration and differentiation of variable order
    • S.G. Samko Fractional integration and differentiation of variable order Analysis Mathematica 21 1995 213 236
    • (1995) Analysis Mathematica , vol.21 , pp. 213-236
    • Samko, S.G.1
  • 19
    • 0013118687 scopus 로고
    • Pseudo differential operators with variable order of differentiation generating Feller semigroup
    • N. Jacob, and H.-G. Leopold Pseudo differential operators with variable order of differentiation generating Feller semigroup Integral Equations and Operator Theory 17 1993 544 553
    • (1993) Integral Equations and Operator Theory , vol.17 , pp. 544-553
    • Jacob, N.1    Leopold, H.-G.2
  • 21
    • 0013161462 scopus 로고    scopus 로고
    • On Markov process generated by pseudodifferential operator of variable order
    • K. Kikuchi, and A. Negoro On Markov process generated by pseudodifferential operator of variable order Osaka Journal of Mathematics 34 1997 319 335
    • (1997) Osaka Journal of Mathematics , vol.34 , pp. 319-335
    • Kikuchi, K.1    Negoro, A.2
  • 24
    • 0036650957 scopus 로고    scopus 로고
    • Variable order and distributed order fractional operators
    • C.F. Lorenzo, and T.T. Hartley Variable order and distributed order fractional operators Nonlinear Dynamics 29 2002 57 98
    • (2002) Nonlinear Dynamics , vol.29 , pp. 57-98
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 25
    • 10144243375 scopus 로고    scopus 로고
    • Control of damping oscilations by fractional differential operator with time-dependent order
    • D. Ingman, and J. Suzdalnitsky Control of damping oscilations by fractional differential operator with time-dependent order Computer Methods in Applied Mechanics and Engineering 193 2004 5585 5595
    • (2004) Computer Methods in Applied Mechanics and Engineering , vol.193 , pp. 5585-5595
    • Ingman, D.1    Suzdalnitsky, J.2
  • 27
    • 84862843990 scopus 로고    scopus 로고
    • On the selection and meaning of variable order operators for dynamic modeling
    • 10.1155/2010/846107 Article ID 846107, 16 pages
    • L.E.S. Ramirez, and C.F.M. Coimbra On the selection and meaning of variable order operators for dynamic modeling International Journal of Differential Equations 2010 2010 10.1155/2010/846107 Article ID 846107, 16 pages
    • (2010) International Journal of Differential Equations , vol.2010
    • Ramirez, L.E.S.1    Coimbra, C.F.M.2
  • 28
    • 67349098149 scopus 로고    scopus 로고
    • Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation
    • R. Lin, F. Liu, V. Anh, and I. Turner Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation Applied Mathematics and Computation 212 2009 435 445
    • (2009) Applied Mathematics and Computation , vol.212 , pp. 435-445
    • Lin, R.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 29
    • 84907893973 scopus 로고    scopus 로고
    • Numerical methods for the variable-order fractional advection-diffusion equation with anonlinear source term
    • P. Zhuang, F. Liu, V. Anh, and I. Turner Numerical methods for the variable-order fractional advection-diffusion equation with anonlinear source term SIAM Journal on Numerical Analysis 47 3 2009 1760 1781
    • (2009) SIAM Journal on Numerical Analysis , vol.47 , Issue.3 , pp. 1760-1781
    • Zhuang, P.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 30
    • 77955704784 scopus 로고    scopus 로고
    • Numerical schemes with high spatial accuracy for a variable-order anomalous subdiffusion equation
    • C. Chen, F. Liu, V. Anh, and I. Turner Numerical schemes with high spatial accuracy for a variable-order anomalous subdiffusion equation SIAM Journal on Scientific Computing 32 4 2010 1740 1760
    • (2010) SIAM Journal on Scientific Computing , vol.32 , Issue.4 , pp. 1740-1760
    • Chen, C.1    Liu, F.2    Anh, V.3    Turner, I.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.