메뉴 건너뛰기




Volumn 36, Issue 9, 2012, Pages 1344-1352

Kernel-based approximation for Cauchy problem of the time-fractional diffusion equation

Author keywords

Cauchy problem of time fractional diffusion equation; Fundamental solution; Inverse Laplace transform; Kernel based approximation; L curve; Tikhonov regularization

Indexed keywords

FUNDAMENTAL SOLUTIONS; INVERSE LAPLACE TRANSFORM; KERNEL-BASED APPROXIMATION; L-CURVE; TIKHONOV REGULARIZATION; TIME-FRACTIONAL DIFFUSION;

EID: 84859376842     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2012.03.003     Document Type: Article
Times cited : (36)

References (44)
  • 1
    • 0000078998 scopus 로고    scopus 로고
    • From continuous time random walks to the fractional Fokker-Planck equation
    • E. Barkai, R. Metzler, and J. Klafter From continuous time random walks to the fractional Fokker-Planck equation Phys Rev E 61 2000 132 138
    • (2000) Phys Rev e , vol.61 , pp. 132-138
    • Barkai, E.1    Metzler, R.2    Klafter, J.3
  • 2
    • 0000914304 scopus 로고
    • Transport aspects in anomalous diffusion
    • Blumen A, Zumofen G, Klafter J. Transport aspects in anomalous diffusion: Levy walks. 1989;40:3964-73.
    • (1989) Levy Walks , vol.40 , pp. 3964-3973
    • Blumen, A.1    Zumofen, G.2    Klafter, J.3
  • 3
    • 84860480019 scopus 로고    scopus 로고
    • Programs for fast numerical inversion of Laplace transforms in MATLAB language environment
    • Brančík L. Programs for fast numerical inversion of Laplace transforms in MATLAB language environment. In: Proceedings of the seventh conference MATLAB99; 2001. p. 352-5.
    • (2001) Proceedings of the Seventh Conference MATLAB99 , pp. 352-355
    • Brančík, L.1
  • 4
    • 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
  • 5
    • 0002745423 scopus 로고    scopus 로고
    • A fractional diffusion equation to describe Levy flights
    • A.S. Chaves A fractional diffusion equation to describe Levy flights Phys Lett A 239 1998 13 16
    • (1998) Phys Lett A , vol.239 , pp. 13-16
    • Chaves, A.S.1
  • 6
    • 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
  • 7
    • 0032155239 scopus 로고    scopus 로고
    • Analytical study and numerical experiments for Laplace equation with overspecified boundary conditions
    • J.T. Chen, and K.H. Chen Analytical study and numerical experiments for Laplace equation with overspecified boundary conditions Appl Math Model 22 1998 703 725
    • (1998) Appl Math Model , vol.22 , pp. 703-725
    • Chen, J.T.1    Chen, K.H.2
  • 8
    • 0029479618 scopus 로고
    • Application of Cesaro mean and the L-curve for the deconvolution problem
    • L.Y. Chen, J.T. Chen, H.K. Chen, and C.H. Chen Application of Cesaro mean and the L-curve for the deconvolution problem J Comput Phys 14 5 1995 361 373
    • (1995) J Comput Phys , vol.14 , Issue.5 , pp. 361-373
    • Chen, L.Y.1    Chen, J.T.2    Chen, H.K.3    Chen, C.H.4
  • 9
    • 70450198851 scopus 로고    scopus 로고
    • Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation
    • J. Cheng, J. Nakagawa, M. Yamamoto, and T. Yamazaki Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation Inverse Probl 25 11 2009
    • (2009) Inverse Probl , vol.25 , Issue.11
    • Cheng, J.1    Nakagawa, J.2    Yamamoto, M.3    Yamazaki, T.4
  • 10
    • 22844456433 scopus 로고    scopus 로고
    • Uniqueness in the Cauchy problem for the heat equation
    • S.Y. Chung Uniqueness in the Cauchy problem for the heat equation Proc Edinburgh Math Soc (2) 42 3 1999 455 468
    • (1999) Proc Edinburgh Math Soc (2) , vol.42 , Issue.3 , pp. 455-468
    • Chung, S.Y.1
  • 12
    • 0000570697 scopus 로고
    • Analysis of discrete ill-posed problems by means of the L-curve
    • P.C. Hansen Analysis of discrete ill-posed problems by means of the L-curve SIAM Rev 34 4 1992 561 580
    • (1992) SIAM Rev , vol.34 , Issue.4 , pp. 561-580
    • Hansen, P.C.1
  • 14
    • 13344267706 scopus 로고
    • Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
    • P.C. Hansen Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems Numer Algorithms 6 1-2 1994 1 35
    • (1994) Numer Algorithms , vol.6 , Issue.12 , pp. 1-35
    • Hansen, P.C.1
  • 15
    • 67549147156 scopus 로고    scopus 로고
    • A discrepancy principle for the source points location in using the MFS for solving the BHCP
    • Y.C. Hon, and M. Li A discrepancy principle for the source points location in using the MFS for solving the BHCP Int J Comput Methods 6 2 2009 181 197
    • (2009) Int J Comput Methods , vol.6 , Issue.2 , pp. 181-197
    • Hon, Y.C.1    Li, M.2
  • 16
    • 40849098576 scopus 로고    scopus 로고
    • Solvability of partial differential equations by meshless kernel methods
    • Y.C. Hon, and R. Schaback Solvability of partial differential equations by meshless kernel methods Adv Comput Math 28 3 2008 283 299
    • (2008) Adv Comput Math , vol.28 , Issue.3 , pp. 283-299
    • Hon, Y.C.1    Schaback, R.2
  • 17
    • 1842842972 scopus 로고    scopus 로고
    • A fundamental solution method for inverse heat conduction problem
    • Y.C. Hon, and T. Wei A fundamental solution method for inverse heat conduction problem Eng Anal Boundary Elem 28 5 2004 489 495
    • (2004) Eng Anal Boundary Elem , vol.28 , Issue.5 , pp. 489-495
    • Hon, Y.C.1    Wei, T.2
  • 18
    • 0342955473 scopus 로고    scopus 로고
    • A numerical computation for inverse boundary determination problem
    • Y.C. Hon, and Z.M. Wu A numerical computation for inverse boundary determination problem Eng Anal Boundary Elem 24 7-8 2000 599 606
    • (2000) Eng Anal Boundary Elem , vol.24 , Issue.78 , pp. 599-606
    • Hon, Y.C.1    Wu, Z.M.2
  • 19
    • 79957534384 scopus 로고    scopus 로고
    • A survey of applications of the MFS to inverse problems
    • A. Karageorghis, D. Lesnic, and L. Marin A survey of applications of the MFS to inverse problems Inverse Probl Sci Eng 19 3 2011 309 336
    • (2011) Inverse Probl Sci Eng , vol.19 , Issue.3 , pp. 309-336
    • Karageorghis, A.1    Lesnic, D.2    Marin, L.3
  • 22
    • 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
  • 23
    • 77957906609 scopus 로고    scopus 로고
    • A backward problem for the time-fractional diffusion equation
    • J.J. Liu, and M. Yamamoto A backward problem for the time-fractional diffusion equation Appl Anal 89 11 2010 1769 1788
    • (2010) Appl Anal , vol.89 , Issue.11 , pp. 1769-1788
    • Liu, J.J.1    Yamamoto, M.2
  • 24
    • 67650855334 scopus 로고    scopus 로고
    • Algorithms for evaluation of the Wright function for the real arguments values
    • Yu.F. Luchko Algorithms for evaluation of the Wright function for the real arguments values Fractional Calc Appl Anal: Int J Theory Appl 11 1 2008 57 75
    • (2008) Fractional Calc Appl Anal: Int J Theory Appl , vol.11 , Issue.1 , pp. 57-75
    • Luchko, Yu.F.1
  • 25
    • 76449091249 scopus 로고    scopus 로고
    • Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation
    • Yu.F. Luchko Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation Comput Math Appl 59 5, Sp. Iss. SI 2010 1766 1772
    • (2010) Comput Math Appl , vol.59 , Issue.SP. ISS. SI 5 , pp. 1766-1772
    • Luchko, Yu.F.1
  • 26
    • 78650789902 scopus 로고    scopus 로고
    • The M-Wright function in time-fractional diffusion processes: A tutorial survey
    • pages Art. ID 104505
    • F. Mainardi, A. Mura, and G. Pagnini The M-Wright function in time-fractional diffusion processes: a tutorial survey Int J Differential Equations 29 2010 pages Art. ID 104505
    • (2010) Int J Differential Equations , vol.29
    • Mainardi, F.1    Mura, A.2    Pagnini, G.3
  • 27
    • 33747807970 scopus 로고    scopus 로고
    • Fractional vector calculus for fractional advection-dispersion
    • M.M. Meerschaert, J. Mortensen, and S.W. Wheatcraft Fractional vector calculus for fractional advection-dispersion Phys A: Stat Mech Appl 278 181-190 2006 181 190
    • (2006) Phys A: Stat Mech Appl , vol.278 , Issue.181-190 , pp. 181-190
    • Meerschaert, M.M.1    Mortensen, J.2    Wheatcraft, S.W.3
  • 28
    • 0033884660 scopus 로고    scopus 로고
    • Boundary value problems for fractional diffusion equations
    • R. Metzler, and J. Klafter Boundary value problems for fractional diffusion equations Phys A: Stat Mech Appl 278 1-2 2000 107 125
    • (2000) Phys A: Stat Mech Appl , vol.278 , Issue.12 , pp. 107-125
    • Metzler, R.1    Klafter, J.2
  • 29
    • 34249102276 scopus 로고    scopus 로고
    • Stable numerical solution of a fractional-diffusion inverse heat conduction problem
    • D.A. Murio Stable numerical solution of a fractional-diffusion inverse heat conduction problem Comput Math Appl: Int J 53 10 2007 1492 1501
    • (2007) Comput Math Appl: Int J , vol.53 , Issue.10 , pp. 1492-1501
    • Murio, D.A.1
  • 30
    • 52049116300 scopus 로고    scopus 로고
    • Time fractional IHCP with Caputo fractional derivatives
    • D.A. Murio Time fractional IHCP with Caputo fractional derivatives Comput Math Appl 56 9 2008 2371 2381
    • (2008) Comput Math Appl , vol.56 , Issue.9 , pp. 2371-2381
    • Murio, D.A.1
  • 31
    • 79951781633 scopus 로고    scopus 로고
    • Overview to mathematical analysis for fractional diffusion equations - New mathematical aspects motivated by industrial collaboration
    • J. Nakagawa, K. Sakamoto, and M. Yamamoto Overview to mathematical analysis for fractional diffusion equations - new mathematical aspects motivated by industrial collaboration J Math Ind (JMI) 2A 2010 99 108
    • (2010) J Math Ind (JMI) , vol.2 A , pp. 99-108
    • Nakagawa, J.1    Sakamoto, K.2    Yamamoto, M.3
  • 32
    • 72549103929 scopus 로고    scopus 로고
    • An ill-posed problem for the heat equation
    • L.E. Payne, and G.A. Philippin An ill-posed problem for the heat equation Math Models Methods Appl Sci 19 9 2009 1631 1641
    • (2009) Math Models Methods Appl Sci , vol.19 , Issue.9 , pp. 1631-1641
    • Payne, L.E.1    Philippin, G.A.2
  • 34
    • 0003797958 scopus 로고    scopus 로고
    • Academic Press Inc. San Diego, CA [An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications]
    • I. Podlubny Fractional differential equations: mathematics in science and engineering vol. 198 1999 Academic Press Inc. San Diego, CA [An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications]
    • (1999) Fractional Differential Equations: Mathematics in Science and Engineering , vol.198
    • Podlubny, I.1
  • 35
    • 0036949980 scopus 로고    scopus 로고
    • Waiting-times and returns in high-frequency financial data: An empirical study
    • M. Raberto, E. Scalas, and F. Mainardi Waiting-times and returns in high-frequency financial data: an empirical study Physica A 314 2002 749 755
    • (2002) Physica A , vol.314 , pp. 749-755
    • Raberto, M.1    Scalas, E.2    Mainardi, F.3
  • 37
    • 40049104874 scopus 로고    scopus 로고
    • Convergence of unsymmetric kernel-based meshless collocation methods
    • R. Schaback Convergence of unsymmetric kernel-based meshless collocation methods SIAM J Numer Anal 45 1 2007 333 351
    • (2007) SIAM J Numer Anal , vol.45 , Issue.1 , pp. 333-351
    • Schaback, R.1
  • 38
    • 79251595176 scopus 로고    scopus 로고
    • Application of numerical inverse Laplace transform algorithms in fractional calculus
    • H. Sheng, Y. Li, and Y.Q. Chen Application of numerical inverse Laplace transform algorithms in fractional calculus J Franklin Inst: Eng Appl Math 348 2 2011 315 330
    • (2011) J Franklin Inst: Eng Appl Math , vol.348 , Issue.2 , pp. 315-330
    • Sheng, H.1    Li, Y.2    Chen, Y.Q.3
  • 39
    • 30744474991 scopus 로고    scopus 로고
    • A full discrete difference scheme for a diffusion-wave system
    • Z.Z. Sun, and X.N. Wu A full discrete difference scheme for a diffusion-wave system Appl Numer Math 56 2006 193 209
    • (2006) Appl Numer Math , vol.56 , pp. 193-209
    • Sun, Z.Z.1    Wu, X.N.2
  • 40
    • 0013298158 scopus 로고    scopus 로고
    • The use of monotonicity for choosing the regularization parameter in ill-posed problems
    • U. Tautenhahn, and U. Hamarik The use of monotonicity for choosing the regularization parameter in ill-posed problems Inverse Probl 15 6 1999 1487 1505
    • (1999) Inverse Probl , vol.15 , Issue.6 , pp. 1487-1505
    • Tautenhahn, U.1    Hamarik, U.2
  • 41
    • 0003664883 scopus 로고
    • V. H. Winston & Sons, John Wiley & Sons Washington, D.C., New York [Translated from the Russian, Preface by translation editor Fritz John, Scripta Series in Mathematics]
    • A.N. Tikhonov, and V.Y. Arsenin Solutions of ill-posed problems 1977 V. H. Winston & Sons, John Wiley & Sons Washington, D.C., New York [Translated from the Russian, Preface by translation editor Fritz John, Scripta Series in Mathematics]
    • (1977) Solutions of Ill-posed Problems
    • Tikhonov, A.N.1    Arsenin, V.Y.2
  • 42
    • 84860463958 scopus 로고    scopus 로고
    • Meshless computation for partial differential equations of fractional order
    • P.H. Wen, and Y.C. Hon Meshless computation for partial differential equations of fractional order WIT Trans Modelling Simulation 52 2011 333 343
    • (2011) WIT Trans Modelling Simulation , vol.52 , pp. 333-343
    • Wen, P.H.1    Hon, Y.C.2
  • 43
    • 79951779651 scopus 로고    scopus 로고
    • Inverse source problem for a fractional diffusion equation
    • Y. Zhang, and X. Xu Inverse source problem for a fractional diffusion equation Inverse Probl 27 3 2011
    • (2011) Inverse Probl , vol.27 , Issue.3
    • Zhang, Y.1    Xu, X.2
  • 44
    • 77956262853 scopus 로고    scopus 로고
    • Spectral regularization method for the time fractional inverse advection-dispersion equation
    • G.H. Zheng, and T. Wei Spectral regularization method for the time fractional inverse advection-dispersion equation Math Comput Simulation 81 1 2010 37 51
    • (2010) Math Comput Simulation , vol.81 , Issue.1 , pp. 37-51
    • Zheng, G.H.1    Wei, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.