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Volumn 228, Issue 2, 2009, Pages 548-560

Explicit methods for fractional differential equations and their stability properties

Author keywords

Differential equation; Explicit method; Fractional order; Interval of stability; Multistep method; Region of stability

Indexed keywords

EXPLICIT METHOD; FRACTIONAL ORDER; INTERVAL OF STABILITY; MULTISTEP METHOD; REGION OF STABILITY;

EID: 64549112216     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.03.025     Document Type: Article
Times cited : (101)

References (18)
  • 1
    • 0037402051 scopus 로고    scopus 로고
    • A fractional trapezoidal rule for integro-differential equations of fractional order in Banach spaces
    • Cuesta E., and Palencia C. A fractional trapezoidal rule for integro-differential equations of fractional order in Banach spaces. Appl. Numer. Math. 45 2-3 (2003) 139-159
    • (2003) Appl. Numer. Math. , vol.45 , Issue.2-3 , pp. 139-159
    • Cuesta, E.1    Palencia, C.2
  • 2
    • 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. 5 (1997) 1-6
    • (1997) Electron. Trans. Numer. Anal. , vol.5 , pp. 1-6
    • Diethelm, K.1
  • 3
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • Diethelm K., and Ford N.J. Analysis of fractional differential equations. J. Math. Anal. Appl. 265 2 (2002) 229-248
    • (2002) J. Math. Anal. Appl. , vol.265 , Issue.2 , pp. 229-248
    • Diethelm, K.1    Ford, N.J.2
  • 4
    • 26444438049 scopus 로고    scopus 로고
    • Pitfalls in fast numerical solvers for fractional differential equations
    • Diethelm K., Ford J.M., Ford N.J., and Weilbeer M. Pitfalls in fast numerical solvers for fractional differential equations. J. Comput. Appl. Math. 186 2 (2006) 482-503
    • (2006) J. Comput. Appl. Math. , vol.186 , Issue.2 , pp. 482-503
    • Diethelm, K.1    Ford, J.M.2    Ford, N.J.3    Weilbeer, M.4
  • 5
    • 64549102866 scopus 로고    scopus 로고
    • A numerical approach for Joulin's model of a point source initiated flame
    • Diethelm K., and Weilbeer M. A numerical approach for Joulin's model of a point source initiated flame. Fract. Calc. Appl. Anal. 7 2 (2004) 191-212
    • (2004) Fract. Calc. Appl. Anal. , vol.7 , Issue.2 , pp. 191-212
    • Diethelm, K.1    Weilbeer, M.2
  • 6
    • 4043168480 scopus 로고    scopus 로고
    • Mixed collocation for fractional differential equations
    • Dubois F., and Mengué S. Mixed collocation for fractional differential equations. Numer. Algorithms 34 2-4 (2003) 303-311
    • (2003) Numer. Algorithms , vol.34 , Issue.2-4 , pp. 303-311
    • Dubois, F.1    Mengué, S.2
  • 8
    • 33646341532 scopus 로고    scopus 로고
    • Comparison of numerical methods for fractional differential equations
    • Ford N.J., and Connolly J.A. Comparison of numerical methods for fractional differential equations. Commun. Pure Appl. Anal. 5 2 (2006) 289-306
    • (2006) Commun. Pure Appl. Anal. , vol.5 , Issue.2 , pp. 289-306
    • Ford, N.J.1    Connolly, J.A.2
  • 9
    • 33751534763 scopus 로고    scopus 로고
    • On multistep methods for differential equations of fractional order
    • Galeone L., and Garrappa R. On multistep methods for differential equations of fractional order. Mediterr. J. Math. 3 3-4 (2006) 565-580
    • (2006) Mediterr. J. Math. , vol.3 , Issue.3-4 , pp. 565-580
    • Galeone, L.1    Garrappa, R.2
  • 10
    • 64549102401 scopus 로고    scopus 로고
    • Second order multistep methods for fractional differential equations
    • Technical Report 20/, Department of Mathematics, University of Bari
    • L. Galeone, R. Garrappa, Second order multistep methods for fractional differential equations, Technical Report 20/2007, Department of Mathematics, University of Bari, 2007
    • (2007) , pp. 2007
    • Galeone, L.1    Garrappa, R.2
  • 11
    • 33846838187 scopus 로고    scopus 로고
    • Discrete models of time-fractional diffusion in a potential well
    • Gorenflo R., and Abdel-Rehim E.A. Discrete models of time-fractional diffusion in a potential well. Fract. Calc. Appl. Anal. 8 2 (2005) 173-200
    • (2005) Fract. Calc. Appl. Anal. , vol.8 , Issue.2 , pp. 173-200
    • Gorenflo, R.1    Abdel-Rehim, E.A.2
  • 12
    • 84950202291 scopus 로고
    • Point-source initiation of lean spherical flames of light reactants: An asymptotic theory
    • Joulin G. Point-source initiation of lean spherical flames of light reactants: An asymptotic theory. Combustion Sci. Technol. 43 (1985) 99-113
    • (1985) Combustion Sci. Technol. , vol.43 , pp. 99-113
    • Joulin, G.1
  • 14
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • Lubich C. Discretized fractional calculus. SIAM J. Math. Anal. 17 3 (1986) 704-719
    • (1986) SIAM J. Math. Anal. , vol.17 , Issue.3 , pp. 704-719
    • Lubich, C.1
  • 15
    • 0041938913 scopus 로고
    • A stability analysis of convolution quadratures for Abel-Volterra integral equations
    • Lubich C. A stability analysis of convolution quadratures for Abel-Volterra integral equations. IMA J. Numer. Anal. 6 1 (1986) 87-101
    • (1986) IMA J. Numer. Anal. , vol.6 , Issue.1 , pp. 87-101
    • Lubich, C.1
  • 17
    • 0003244044 scopus 로고    scopus 로고
    • Fractional differential equations
    • Academic Press Inc., San Diego, CA
    • Podlubny I. Fractional differential equations. Mathematics in Science and Engineering vol. 198 (1999), Academic Press Inc., San Diego, CA
    • (1999) Mathematics in Science and Engineering , vol.198
    • Podlubny, I.1
  • 18
    • 25444472344 scopus 로고    scopus 로고
    • An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations
    • Yuste S.B., and Acedo L. An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations. SIAM J. Numer. Anal. 42 5 (2005) 1862-1874
    • (2005) SIAM J. Numer. Anal. , vol.42 , Issue.5 , pp. 1862-1874
    • Yuste, S.B.1    Acedo, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.