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Volumn 22, Issue 4, 2012, Pages

Stability-preserving high-order methods for multiterm fractional differential equations

Author keywords

accuracy; Fractional differential equation; multiterm equation; Runge Kutta method; stability

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; CONVOLUTION; DIFFERENTIAL EQUATIONS; LAPLACE TRANSFORMS; NUMERICAL METHODS; STABILITY;

EID: 84861212214     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127412500733     Document Type: Article
Times cited : (18)

References (26)
  • 1
    • 0001028358 scopus 로고
    • An inverse matrix adjustment arising in discriminant analysis
    • Bartlett, M S. [1951] "An inverse matrix adjustment arising in discriminant analysis," Ann. Math. Statist. 22, 107-111
    • (1951) Ann. Math. Statist. , vol.22 , pp. 107-111
    • Bartlett, M.S.1
  • 2
    • 0001110962 scopus 로고    scopus 로고
    • Coprime factorizations and stability of fractional differential systems
    • Bonnet, C & Partington, J. R. [2000] "Coprime factorizations and stability of fractional differential systems," Syst. Contr. Lett. 41, 167-174
    • (2000) Syst. Contr. Lett. , vol.41 , pp. 167-174
    • Bonnet, C.1    Partington, J.R.2
  • 5
    • 33748663764 scopus 로고    scopus 로고
    • Numerical solution of linear multi-term initial value problems of fractional order
    • Diethelm, K & Luchko, Y. [2004] "Numerical solution of linear multi-term initial value problems of fractional order," J. Comput. Anal. Appl. 6, 243-263
    • (2004) J. Comput. Anal. Appl. , vol.6 , pp. 243-263
    • Diethelm, K.1    Luchko, Y.2
  • 6
    • 77950859639 scopus 로고    scopus 로고
    • Order conditions for Volterra Runge-Kutta methods
    • Garrappa, R. [2010] "Order conditions for Volterra Runge-Kutta methods," Appl Numer. Math. 60, 561-573
    • (2010) Appl Numer. Math. , vol.60 , pp. 561-573
    • Garrappa, R.1
  • 7
    • 79961015107 scopus 로고    scopus 로고
    • Generalized exponential time differencing methods for fractional order problems
    • Garrappa, R & Popolizio,M. [2011a] "Generalized exponential time differencing methods for fractional order problems," Comput. Math. Appl. 62, 876-890
    • (2011) Comput. Math. Appl. , vol.62 , pp. 876-890
    • Garrappa, R.1    Popoliziom2
  • 8
    • 77957868556 scopus 로고    scopus 로고
    • On accurate product integration rules for linear fractional differential equations
    • Garrappa, R & Popolizio, M. [2011b] "On accurate product integration rules for linear fractional differential equations," J. Comput. Appl. Math. 235, 1085-1097
    • (2011) J. Comput. Appl. Math. , vol.235 , pp. 1085-1097
    • Garrappa, R.1    Popolizio, M.2
  • 9
    • 0002847893 scopus 로고    scopus 로고
    • Fractional calculus: Integral and differential equations of fractional order
    • reprinted with revisions in
    • Gorenflo, R & Mainardi, F. [1997] "Fractional calculus: Integral and differential equations of fractional order," CISM Courses and Lectures 378, 223-276, reprinted with revisions in http://arxiv.org/abs/0805.3823
    • (1997) CISM Courses and Lectures , vol.378 , pp. 223-276
    • Gorenflo, R.1    Mainardi, F.2
  • 11
    • 0003589989 scopus 로고    scopus 로고
    • Springer Series in Computational Mathematics, 2nd edition (Springer-Verlag, Berlin)
    • Hairer, E & Wanner, G. [1996] Solving Ordinary Differential Equations. II, Springer Series in Computational Mathematics, Vol. 14, 2nd edition (Springer-Verlag, Berlin)
    • (1996) Solving Ordinary Differential Equations. II , vol.14
    • Hairer, E.1    Wanner, G.2
  • 13
    • 22944439754 scopus 로고    scopus 로고
    • Functions preserving matrix groups and iterations for the matrix square root
    • (electronic)
    • Higham, N. J., Mackey, D. S., Mackey, N & Tisseur, F. [2005] "Functions preserving matrix groups and iterations for the matrix square root," SIAM J. Matrix Anal. Appl. 26, 849-877 (electronic)
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , pp. 849-877
    • Higham, N.J.1    Mackey, D.S.2    Mackey, N.3    Tisseur, F.4
  • 14
    • 5144231600 scopus 로고    scopus 로고
    • On the numerical inversion of the Laplace transform of certain holomorphic mappings
    • López-Fernández, M & Palencia, C. [2004] "On the numerical inversion of the Laplace transform of certain holomorphic mappings," Appl. Numer. Math. 51, 289-303
    • (2004) Appl. Numer. Math. , vol.51 , pp. 289-303
    • López-Fernández, M.1    Palencia, C.2
  • 15
    • 33749020865 scopus 로고    scopus 로고
    • A spectral order method for inverting sectorial Laplace transforms
    • (electronic)
    • López-Fernández, M., Palencia, C & Schädle, A. [2006] "A spectral order method for inverting sectorial Laplace transforms," SIAM J. Numer. Anal. 44, 1332-1350 (electronic)
    • (2006) SIAM J. Numer. Anal. , vol.44 , pp. 1332-1350
    • López-Fernández, M.1    Palencia, C.2    Schädle, A.3
  • 17
    • 84962571892 scopus 로고
    • Runge-Kutta theory for Volterra and Abel integral equations of the second kind
    • Lubich, C. [1983] "Runge-Kutta theory for Volterra and Abel integral equations of the second kind," Math Comp. 41, 87-102
    • (1983) Math Comp. , vol.41 , pp. 87-102
    • Lubich, C.1
  • 18
    • 34250092484 scopus 로고
    • Convolution quadrature and discretized operational calculus. I, II
    • 413-425
    • Lubich, C. [1988] "Convolution quadrature and discretized operational calculus. I, II," Numer. Math. 52, 129-145, 413-425
    • (1988) Numer. Math. , vol.52 , pp. 129-145
    • Lubich, C.1
  • 19
    • 84968504982 scopus 로고
    • Runge-Kutta methods for parabolic equations and convolution quadrature
    • Lubich, C & Ostermann, A. [1993] "Runge-Kutta methods for parabolic equations and convolution quadrature," Math Comp. 60, 105-131
    • (1993) Math Comp. , vol.60 , pp. 105-131
    • Lubich, C.1    Ostermann, A.2
  • 20
    • 0000074512 scopus 로고    scopus 로고
    • Stability properties for generalized fractional differential systems
    • Paris 1998) (Soc.Math. Appl. Indust., Paris)
    • Matignon, D. [1998] "Stability properties for generalized fractional differential systems," Systèmes Différentiels Fractionnaires (Paris, 1998) (Soc.Math. Appl. Indust., Paris), pp. 145-158
    • (1998) Systèmes Différentiels Fractionnaires , pp. 145-158
    • Matignon, D.1
  • 22
    • 0041938914 scopus 로고    scopus 로고
    • Diskretisierung von mehrgliedrigen abelschen integralgleichungen und gewöhnlichen differentialgleichungen gebrochener ordnung
    • Berlin
    • Nkamnang, A. R. [1999] "Diskretisierung von mehrgliedrigen abelschen integralgleichungen und gewöhnlichen differentialgleichungen gebrochener ordnung," PhD thesis, Freie Universität Berlin, Berlin
    • (1999) PhD Thesis Freie Universität Berlin
    • Nkamnang, A.R.1
  • 23
    • 0003797958 scopus 로고    scopus 로고
    • Mathematics in Science and Engineering Academic Press Inc., San Diego, CA)
    • Podlubny, I. [1999] Fractional Differential Equations, Mathematics in Science and Engineering, Vol. 198 (Academic Press Inc., San Diego, CA)
    • (1999) Fractional Differential Equations , vol.198
    • Podlubny, I.1
  • 24
    • 0002152334 scopus 로고
    • The accurate numerical inversion of Laplace transforms
    • Talbot, A. [1979] "The accurate numerical inversion of Laplace transforms," J. Inst. Math. Appl. 23, 97-120
    • (1979) J. Inst. Math. Appl. , vol.23 , pp. 97-120
    • Talbot, A.1
  • 25
    • 34548172888 scopus 로고    scopus 로고
    • Optimizing Talbot's contours for the inversion of the Laplace transform
    • (electronic)
    • Weideman, J. A. C. [2006] "Optimizing Talbot's contours for the inversion of the Laplace transform," SIAM J. Numer. Anal. 44, 2342-2362 (electronic)
    • (2006) SIAM J. Numer. Anal. , vol.44 , pp. 2342-2362
    • Weideman, J.A.C.1
  • 26
    • 34548162562 scopus 로고    scopus 로고
    • Parabolic and hyperbolic contours for computing the Bromwich integral
    • (electronic)
    • Weideman, J. A. C & Trefethen, L. N. [2007] "Parabolic and hyperbolic contours for computing the Bromwich integral," Math. Comp. 76, 1341-1356 (electronic).
    • (2007) Math. Comp. , vol.76 , pp. 1341-1356
    • Weideman, J.A.C.1    Trefethen, L.N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.