메뉴 건너뛰기




Volumn 57, Issue , 2015, Pages 37-46

Method of approximate particular solutions for constant- and variable-order fractional diffusion models

Author keywords

Collocation method; Fractional diffusion; Meshless method; Radial basis function

Indexed keywords

FINITE DIFFERENCE METHOD; FUNCTIONS; OPTICAL PROJECTORS; RADIAL BASIS FUNCTION NETWORKS;

EID: 84930374284     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2014.09.003     Document Type: Article
Times cited : (112)

References (50)
  • 2
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • R. Metzler, and J. Klafter The random walk's guide to anomalous diffusion: a fractional dynamics approach Phys Rep 339 1 2000 1 77
    • (2000) Phys Rep , vol.339 , Issue.1 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 3
    • 0009481303 scopus 로고
    • The fractional diffusion equation
    • W. Wyss The fractional diffusion equation J Math Phys 27 1986 2782 2785
    • (1986) J Math Phys , vol.27 , pp. 2782-2785
    • Wyss, W.1
  • 4
    • 0000103589 scopus 로고    scopus 로고
    • Wright functions as scale-invariant solutions of the diffusion-wave equation
    • R. Gorenflo, Y. Luchko, and F. Mainardi Wright functions as scale-invariant solutions of the diffusion-wave equation J Comput Appl Math 118 1-2 2000 175 191
    • (2000) J Comput Appl Math , vol.118 , Issue.1-2 , pp. 175-191
    • Gorenflo, R.1    Luchko, Y.2    Mainardi, F.3
  • 5
    • 79960431454 scopus 로고    scopus 로고
    • Novel numerical methods for solving the time-space fractional diffusion equation in two dimensions
    • Q. Yang, I. Turner, F. Liu, and M. Ilis Novel numerical methods for solving the time-space fractional diffusion equation in two dimensions SIAM J Sci Comput 33 3 2011 1159 1180
    • (2011) SIAM J Sci Comput , vol.33 , Issue.3 , pp. 1159-1180
    • Yang, Q.1    Turner, I.2    Liu, F.3    Ilis, M.4
  • 6
    • 0036828301 scopus 로고    scopus 로고
    • Discrete random walk models for space-time fractional diffusion
    • R. Gorenflo, F. Mainardi, D. Moretti, G. Pagnini, and P. Paradisi Discrete random walk models for space-time fractional diffusion Chem Phys 284 1-2 2007 521 541
    • (2007) Chem Phys , vol.284 , Issue.1-2 , pp. 521-541
    • Gorenflo, R.1    Mainardi, F.2    Moretti, D.3    Pagnini, G.4    Paradisi, P.5
  • 7
    • 84871003930 scopus 로고    scopus 로고
    • Boundary particle method for Laplace transformed time fractional diffusion equations
    • Z.-J. Fu, W. Chen, and H.-T. Yang Boundary particle method for Laplace transformed time fractional diffusion equations J Comput Phys 235 2013 52 66
    • (2013) J Comput Phys , vol.235 , pp. 52-66
    • Fu, Z.-J.1    Chen, W.2    Yang, H.-T.3
  • 9
    • 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 Phys A: Stat Mech Appl 388 21 2009 4586 4592
    • (2009) Phys A: Stat Mech Appl , vol.388 , Issue.21 , pp. 4586-4592
    • Sun, H.1    Chen, W.2    Chen, Y.3
  • 10
    • 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 Dyn 29 1-4 2002 57 98
    • (2002) Nonlinear Dyn , vol.29 , Issue.1-4 , pp. 57-98
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 11
    • 79953691444 scopus 로고    scopus 로고
    • A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems
    • H. Sun, W. Chen, and H. Wei A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems Eur Phys J Spec Top 193 1 2011 185 192
    • (2011) Eur Phys J Spec Top , vol.193 , Issue.1 , pp. 185-192
    • Sun, H.1    Chen, W.2    Wei, H.3
  • 12
    • 33845628108 scopus 로고    scopus 로고
    • A second-order accurate numerical method for the two-dimensional fractional diffusion equation
    • C. Tadjeran, and M.M. Meerschaert A second-order accurate numerical method for the two-dimensional fractional diffusion equation J Comput Phys 220 2 2007 813 823
    • (2007) J Comput Phys , vol.220 , Issue.2 , pp. 813-823
    • Tadjeran, C.1    Meerschaert, M.M.2
  • 13
    • 46049119633 scopus 로고    scopus 로고
    • Implicit finite difference approximation for time fractional diffusion equations
    • D.A. Murio Implicit finite difference approximation for time fractional diffusion equations Comput Math Appl 56 4 2008 1138 1145
    • (2008) Comput Math Appl , vol.56 , Issue.4 , pp. 1138-1145
    • Murio, D.A.1
  • 14
    • 77955927812 scopus 로고    scopus 로고
    • A direct O(Nlog2N) finite difference method for fractional diffusion equations
    • H. Wang, K. Wang, and T. Sircar A direct O(Nlog2N) finite difference method for fractional diffusion equations J Comput Phys 229 21 2010 8095 8104
    • (2010) J Comput Phys , vol.229 , Issue.21 , pp. 8095-8104
    • Wang, H.1    Wang, K.2    Sircar, T.3
  • 15
    • 84868502319 scopus 로고    scopus 로고
    • Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
    • J. Ren, Z. Sun, and X. Zhao Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions J Comput Phys 232 1 2013 456 467
    • (2013) J Comput Phys , vol.232 , Issue.1 , pp. 456-467
    • Ren, J.1    Sun, Z.2    Zhao, X.3
  • 16
    • 79956124918 scopus 로고    scopus 로고
    • A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
    • X. Zhao, and Z. Sun A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions J Comput Phys 230 15 2011 6061 6074
    • (2011) J Comput Phys , vol.230 , Issue.15 , pp. 6061-6074
    • Zhao, X.1    Sun, Z.2
  • 17
    • 84861204912 scopus 로고    scopus 로고
    • Finite difference schemes for variable-order time fractional diffusion equation
    • H. Sun, W. Chen, C. Li, and Y. Chen Finite difference schemes for variable-order time fractional diffusion equation Int J Bifurc Chaos 22 04 2012 1250085
    • (2012) Int J Bifurc Chaos , vol.22 , Issue.4 , pp. 1250085
    • Sun, H.1    Chen, W.2    Li, C.3    Chen, Y.4
  • 18
    • 84862850103 scopus 로고    scopus 로고
    • Numerical techniques for the variable order time fractional diffusion equation
    • S. Shen, F. Liu, J. Chen, I. Turner, and V. Anh Numerical techniques for the variable order time fractional diffusion equation Appl Math Comput 218 22 2012 10861 10870
    • (2012) Appl Math Comput , vol.218 , Issue.22 , pp. 10861-10870
    • Shen, S.1    Liu, F.2    Chen, J.3    Turner, I.4    Anh, V.5
  • 19
    • 77955704784 scopus 로고    scopus 로고
    • Numerical schemes with high spatial accuracy for a variable-order anomalous subdiffusion equation
    • C.M. Chen, F. Liu, V. Anh, and I. Turner Numerical schemes with high spatial accuracy for a variable-order anomalous subdiffusion equation SIAM J Sci Comput 32 4 2010 1740 1760
    • (2010) SIAM J Sci Comput , vol.32 , Issue.4 , pp. 1740-1760
    • Chen, C.M.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 20
    • 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 Appl Math Comput 212 2 2009 435 445
    • (2009) Appl Math Comput , vol.212 , Issue.2 , pp. 435-445
    • Lin, R.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 21
    • 17144427014 scopus 로고    scopus 로고
    • The accuracy and stability of an implicit solution method for the fractional diffusion equation
    • T.A.M. Langlands, and B.I. Henry The accuracy and stability of an implicit solution method for the fractional diffusion equation J Comput Phys 205 2 2005 719 736
    • (2005) J Comput Phys , vol.205 , Issue.2 , pp. 719-736
    • Langlands, T.A.M.1    Henry, B.I.2
  • 22
    • 69049086472 scopus 로고    scopus 로고
    • Compact finite difference method for the fractional diffusion equation
    • M. Cui Compact finite difference method for the fractional diffusion equation J Comput Phys 228 20 2009 7792 7804
    • (2009) J Comput Phys , vol.228 , Issue.20 , pp. 7792-7804
    • Cui, M.1
  • 23
    • 84867978055 scopus 로고    scopus 로고
    • Implicit difference approximation for the time fractional diffusion equation
    • P. Zhuang, and F. Liu Implicit difference approximation for the time fractional diffusion equation J Appl Math Comput 22 3 2006 87 99
    • (2006) J Appl Math Comput , vol.22 , Issue.3 , pp. 87-99
    • Zhuang, P.1    Liu, F.2
  • 24
    • 84865575179 scopus 로고    scopus 로고
    • Compact alternating direction implicit scheme for the two-dimensional fractional diffusion-wave equation
    • Y. Zhang, Z. Sun, and X. Zhao Compact alternating direction implicit scheme for the two-dimensional fractional diffusion-wave equation SIAM J Numer Anal 50 3 2012 1535 1555
    • (2012) SIAM J Numer Anal , vol.50 , Issue.3 , pp. 1535-1555
    • Zhang, Y.1    Sun, Z.2    Zhao, X.3
  • 25
    • 36149001420 scopus 로고    scopus 로고
    • A Fourier method for the fractional diffusion equation describing sub-diffusion
    • C.-M. Chen, F. Liu, I. Turner, and V. Anh A Fourier method for the fractional diffusion equation describing sub-diffusion J Comput Phys 227 2 2007 886 897
    • (2007) J Comput Phys , vol.227 , Issue.2 , pp. 886-897
    • Chen, C.-M.1    Liu, F.2    Turner, I.3    Anh, V.4
  • 26
    • 34547548712 scopus 로고    scopus 로고
    • Finite difference/spectral approximations for the time-fractional diffusion equation
    • Y. Lin, and C. Xu Finite difference/spectral approximations for the time-fractional diffusion equation J Comput Phys 225 2 2007 1533 1552
    • (2007) J Comput Phys , vol.225 , Issue.2 , pp. 1533-1552
    • Lin, Y.1    Xu, C.2
  • 27
    • 79953248728 scopus 로고    scopus 로고
    • High-order finite element methods for time-fractional partial differential equations
    • Y. Jiang, and J. Ma High-order finite element methods for time-fractional partial differential equations J Comput Appl Math 235 11 2011 3285 3290
    • (2011) J Comput Appl Math , vol.235 , Issue.11 , pp. 3285-3290
    • Jiang, Y.1    Ma, J.2
  • 28
    • 79960990048 scopus 로고    scopus 로고
    • Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion
    • C. Li, Z. Zhao, and Y. Chen Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion Comput Math Appl 62 3 2011 855 875
    • (2011) Comput Math Appl , vol.62 , Issue.3 , pp. 855-875
    • Li, C.1    Zhao, Z.2    Chen, Y.3
  • 29
    • 14644446063 scopus 로고    scopus 로고
    • Least squares finite-element solution of a fractional order two-point boundary value problem
    • G.J. Fix, and J.P. Roof Least squares finite-element solution of a fractional order two-point boundary value problem Comput Math Appl 48 7-8 2004 1017 1033
    • (2004) Comput Math Appl , vol.48 , Issue.7-8 , pp. 1017-1033
    • Fix, G.J.1    Roof, J.P.2
  • 30
    • 79960999848 scopus 로고    scopus 로고
    • The BEM for numerical solution of partial fractional differential equations
    • J.T. Katsikadelis The BEM for numerical solution of partial fractional differential equations Comput Math Appl 62 3 2011 891 901
    • (2011) Comput Math Appl , vol.62 , Issue.3 , pp. 891-901
    • Katsikadelis, J.T.1
  • 31
    • 77954142858 scopus 로고    scopus 로고
    • Numerical simulations of 2D fractional subdiffusion problems
    • H. Brunner, L. Ling, and M. Yamamoto Numerical simulations of 2D fractional subdiffusion problems J Comput Phys 229 18 2010 6613 6622
    • (2010) J Comput Phys , vol.229 , Issue.18 , pp. 6613-6622
    • Brunner, H.1    Ling, L.2    Yamamoto, M.3
  • 32
    • 76449113714 scopus 로고    scopus 로고
    • Fractional diffusion equations by the Kansa method
    • W. Chen, L. Ye, and H. Sun Fractional diffusion equations by the Kansa method Comput Math Appl 59 5 2010 1614 1620
    • (2010) Comput Math Appl , vol.59 , Issue.5 , pp. 1614-1620
    • Chen, W.1    Ye, L.2    Sun, H.3
  • 33
    • 79251616666 scopus 로고    scopus 로고
    • An implicit RBF meshless approach for time fractional diffusion equations
    • Q. Liu, Y. Gu, P. Zhuang, F. Liu, and Y. Nie An implicit RBF meshless approach for time fractional diffusion equations Comput Mech 48 1 2011 1 12
    • (2011) Comput Mech , vol.48 , Issue.1 , pp. 1-12
    • Liu, Q.1    Gu, Y.2    Zhuang, P.3    Liu, F.4    Nie, Y.5
  • 34
    • 80052563848 scopus 로고    scopus 로고
    • The method of approximate particular solutions for solving elliptic problems with variable coefficients
    • C.S. Chen, C.M. Fan, and P.H. Wen The method of approximate particular solutions for solving elliptic problems with variable coefficients Int J Comput Methods 8 03 2011 545 559
    • (2011) Int J Comput Methods , vol.8 , Issue.3 , pp. 545-559
    • Chen, C.S.1    Fan, C.M.2    Wen, P.H.3
  • 35
    • 78149248899 scopus 로고    scopus 로고
    • Adaptive method of particular solution for solving 3d inhomogeneous elliptic equations
    • L. Ling, C.S. Chen, and T.O. Kwok Adaptive method of particular solution For solving 3d inhomogeneous elliptic equations Int J Comput Methods 07 03 2010 499 511
    • (2010) Int J Comput Methods , vol.7 , Issue.3 , pp. 499-511
    • Ling, L.1    Chen, C.S.2    Kwok, T.O.3
  • 37
    • 69249217656 scopus 로고    scopus 로고
    • The method of particular solutions for solving axisymmetric polyharmonic and poly-Helmholtz equations
    • C.-C. Tsai, C.S. Chen, and T.-W. Hsu The method of particular solutions for solving axisymmetric polyharmonic and poly-Helmholtz equations Eng Anal Bound Elem 33 12 2009 1396 1402
    • (2009) Eng Anal Bound Elem , vol.33 , Issue.12 , pp. 1396-1402
    • Tsai, C.-C.1    Chen, C.S.2    Hsu, T.-W.3
  • 38
    • 84863021226 scopus 로고    scopus 로고
    • The method of approximate particular solutions for solving certain partial differential equations
    • C.S. Chen, C.M. Fan, and P.H. Wen The method of approximate particular solutions for solving certain partial differential equations Numer Methods Partial Diff Equ 28 2 2012 506 522
    • (2012) Numer Methods Partial Diff Equ , vol.28 , Issue.2 , pp. 506-522
    • Chen, C.S.1    Fan, C.M.2    Wen, P.H.3
  • 39
    • 84891796751 scopus 로고    scopus 로고
    • The method of approximate particular solutions for solving anisotropic elliptic problems
    • H. Zhu The method of approximate particular solutions for solving anisotropic elliptic problems Eng Anal Bound Elem 40 2014 123 127
    • (2014) Eng Anal Bound Elem , vol.40 , pp. 123-127
    • Zhu, H.1
  • 40
    • 84871368342 scopus 로고    scopus 로고
    • Method of particular solutions for nonlinear Poisson-type equations in irregular domains
    • S.Y. Reutskiy Method of particular solutions for nonlinear Poisson-type equations in irregular domains Eng Anal Bound Elem 37 2 2013 401 408
    • (2013) Eng Anal Bound Elem , vol.37 , Issue.2 , pp. 401-408
    • Reutskiy, S.Y.1
  • 41
    • 84890100506 scopus 로고    scopus 로고
    • Domain type kernel-based meshless methods for solving wave equations
    • L.H. Kuo, M.H. Gu, D.L. Young, and C.Y. Lin Domain type kernel-based meshless methods for solving wave equations CMC-Comput Mater Contin 33 3 2013 213 228
    • (2013) CMC-Comput Mater Contin , vol.33 , Issue.3 , pp. 213-228
    • Kuo, L.H.1    Gu, M.H.2    Young, D.L.3    Lin, C.Y.4
  • 42
    • 84878798746 scopus 로고    scopus 로고
    • The global approximate particular solution meshless method for two-dimensional linear elasticity problems
    • C.A. Bustamante, H. Power, W.F. Florez, and C.Y. Hang The global approximate particular solution meshless method for two-dimensional linear elasticity problems Int J Comput Math 90 5 2013 978 993
    • (2013) Int J Comput Math , vol.90 , Issue.5 , pp. 978-993
    • Bustamante, C.A.1    Power, H.2    Florez, W.F.3    Hang, C.Y.4
  • 43
    • 84872607375 scopus 로고    scopus 로고
    • A global meshless collocation particular solution method (integrated radial basis function) for two-dimensional Stokes flow problems
    • C.A. Bustamante, H. Power, Y.H. Sua, and W.F. Florez A global meshless collocation particular solution method (integrated radial basis function) for two-dimensional Stokes flow problems Appl Math Modell 37 6 2013 4538 4547
    • (2013) Appl Math Modell , vol.37 , Issue.6 , pp. 4538-4547
    • Bustamante, C.A.1    Power, H.2    Sua, Y.H.3    Florez, W.F.4
  • 44
    • 84863145066 scopus 로고    scopus 로고
    • The method of particular solutions for solving inverse problems of a nonhomogeneous convection-diffusion equation with variable coefficients
    • T. Jiang, M. Li, and C.S. Chen The method of particular solutions for solving inverse problems of a nonhomogeneous convection-diffusion equation with variable coefficients Numer Heat Transf, Part A: Appl 61 5 2012 338 352
    • (2012) Numer Heat Transf, Part A: Appl , vol.61 , Issue.5 , pp. 338-352
    • Jiang, T.1    Li, M.2    Chen, C.S.3
  • 45
    • 84862321370 scopus 로고    scopus 로고
    • Assessment of global and local meshless methods based on collocation with radial basis functions for parabolic partial differential equations in three dimensions
    • G. Yao, I. Siraj ul, and B. Sarler Assessment of global and local meshless methods based on collocation with radial basis functions for parabolic partial differential equations in three dimensions Eng Anal Bound Elem 36 11 2012 1640 1648
    • (2012) Eng Anal Bound Elem , vol.36 , Issue.11 , pp. 1640-1648
    • Yao, G.1    Siraj Ul, I.2    Sarler, B.3
  • 46
    • 84880437906 scopus 로고    scopus 로고
    • Method of particular solutions for solving PDEs of the second and fourth orders with variable coefficients
    • S.Y. Reutskiy Method of particular solutions for solving PDEs of the second and fourth orders with variable coefficients Eng Anal Bound Elem 37 10 2013 1305 1310
    • (2013) Eng Anal Bound Elem , vol.37 , Issue.10 , pp. 1305-1310
    • Reutskiy, S.Y.1
  • 47
    • 84878324963 scopus 로고    scopus 로고
    • A global meshless collocation particular solution method for solving the two-dimensional Navier-Stokes system of equations
    • C.A. Bustamante, H. Power, and W.F. Florez A global meshless collocation particular solution method for solving the two-dimensional Navier-Stokes system of equations Comput Math Appl 65 12 2013 1939 1955
    • (2013) Comput Math Appl , vol.65 , Issue.12 , pp. 1939-1955
    • Bustamante, C.A.1    Power, H.2    Florez, W.F.3
  • 49
    • 33646398146 scopus 로고    scopus 로고
    • Convolution quadrature time discretization of fractional diffusion-wave equations
    • E. Cuesta, C. Lubich, and C. Palencia Convolution quadrature time discretization of fractional diffusion-wave equations Math Comput 75 254 2006 673 696
    • (2006) Math Comput , vol.75 , Issue.254 , pp. 673-696
    • Cuesta, E.1    Lubich, C.2    Palencia, C.3
  • 50
    • 0001097696 scopus 로고    scopus 로고
    • Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes
    • Jameson A, Schmidt W, Turkel E. Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. AIAA paper; 1981-1259.
    • AIAA Paper , pp. 1981-1259
    • Jameson, A.1    Schmidt, W.2    Turkel, E.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.