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Volumn 75, Issue 254, 2006, Pages 673-696

Convolution quadrature time discretization of fractional diffusion-wave equations

Author keywords

Anomalous diffusion; Convolution quadrature; Error analysis; Fractional BDF method; Parabolic equation with memory; Regularity; Time discretization

Indexed keywords


EID: 33646398146     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-06-01788-1     Document Type: Article
Times cited : (287)

References (37)
  • 2
    • 0141976345 scopus 로고    scopus 로고
    • Maximum-norm estimates for resolvents of elliptic finite element operators
    • MR1986795 (2004g:65074)
    • N. Y. Bakaev, V. Thomée, and L. Wahlbin, Maximum-norm estimates for resolvents of elliptic finite element operators, Math. Comp. 72 (2002) 1597-1610. MR1986795 (2004g:65074)
    • (2002) Math. Comp. , vol.72 , pp. 1597-1610
    • Bakaev, N.Y.1    Thomée, V.2    Wahlbin, L.3
  • 3
    • 0036792332 scopus 로고    scopus 로고
    • Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems
    • MR1933043 (2003h:65091)
    • M. P. Calvo and C. Palencia, Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems, Math. Comp. 71 (2001) 1529-1543. MR1933043 (2003h:65091)
    • (2001) Math. Comp. , vol.71 , pp. 1529-1543
    • Calvo, M.P.1    Palencia, C.2
  • 5
    • 84968521959 scopus 로고
    • Finite element approximation of a parabolic integro-differential equation with a weakly singular kernel
    • MR1122059 (93g:65120)
    • C. Cheng, V. Thomée, and L. Wahlbin, Finite element approximation of a parabolic integro-differential equation with a weakly singular kernel, Math. Comp. 58 (1992) 587-602. MR1122059 (93g:65120)
    • (1992) Math. Comp. , vol.58 , pp. 587-602
    • Cheng, C.1    Thomée, V.2    Wahlbin, L.3
  • 6
    • 0023450854 scopus 로고
    • On multistep approximation of semigroups in Banach spaces
    • MR0920377 (88j:65135)
    • M. Crouzeix, On multistep approximation of semigroups in Banach spaces, J. Comput. Appl. Math. 20 (1987) 25-35. MR0920377 (88j:65135)
    • (1987) J. Comput. Appl. Math. , vol.20 , pp. 25-35
    • Crouzeix, M.1
  • 7
    • 0037402051 scopus 로고    scopus 로고
    • A fractional trapezoidal rule for integro-differential equations of fractional order in Banach spaces
    • MR1967571 (2004b:65210)
    • E. Cuesta and C. Palencia, A fractional trapezoidal rule for integro-differential equations of fractional order in Banach spaces, Appl. Numer. Math. 45 (2003) 139-159. MR1967571 (2004b:65210)
    • (2003) Appl. Numer. Math. , vol.45 , pp. 139-159
    • Cuesta, E.1    Palencia, C.2
  • 8
    • 4544380424 scopus 로고    scopus 로고
    • A numerical method for an integro-differential equation with memory in Banach spaces: Qualitative properties
    • MR2034878 (2004m:65225)
    • E. Cuesta and C. Palencia, A numerical method for an integro-differential equation with memory in Banach spaces: Qualitative properties, SIAM J. Numer. Anal. 41 (2003) 1232-1241. MR2034878 (2004m:65225)
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 1232-1241
    • Cuesta, E.1    Palencia, C.2
  • 9
    • 84972571026 scopus 로고
    • Integro-differential equation which interpolates the heat equation and the wave equation
    • MR1066629 (91i:45007)
    • Y. Fujita, Integro-differential equation which interpolates the heat equation and the wave equation, Osaka J. Math. 27 (1990) 319-327. MR1066629 (91i:45007)
    • (1990) Osaka J. Math. , vol.27 , pp. 319-327
    • Fujita, Y.1
  • 10
    • 84972571026 scopus 로고
    • Integro-differential equation which interpolates the heat equation and the wave equation (II)
    • MR1088183 (92a:45032)
    • Y. Fujita, Integro-differential equation which interpolates the heat equation and the wave equation (II), Osaka J. Math. 27 (1990) 797-804. MR1088183 (92a:45032)
    • (1990) Osaka J. Math. , vol.27 , pp. 797-804
    • Fujita, Y.1
  • 11
    • 0039756624 scopus 로고    scopus 로고
    • Stability of Runge-Kutta methods for abstract time-dependent parabolic problems: The Hölder case
    • MR1609666 (99c:65108)
    • C. González and C. Palencia, Stability of Runge-Kutta methods for abstract time-dependent parabolic problems: the Hölder case, Math. Comp. 68 (1999) 73-89. MR1609666 (99c:65108)
    • (1999) Math. Comp. , vol.68 , pp. 73-89
    • González, C.1    Palencia, C.2
  • 12
    • 0035813991 scopus 로고    scopus 로고
    • Wave propagation in media with singular memory
    • MR1868410 (2002m:74028)
    • A. Hanyga, Wave propagation in media with singular memory, Math. Comput. Model. 34 (2001) 1399-1421. MR1868410 (2002m:74028)
    • (2001) Math. Comput. Model. , vol.34 , pp. 1399-1421
    • Hanyga, A.1
  • 13
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer, Berlin. MR0610244 (83j:35084)
    • D. Henry, Geometric Theory of Semilinear Parabolic Equations, LNM 840, Springer, Berlin (1981). MR0610244 (83j:35084)
    • (1981) LNM , vol.840
    • Henry, D.1
  • 14
    • 0003427295 scopus 로고    scopus 로고
    • R. Hilfer (ed.), World Scientific, Singapore. MR1890104 (2002j:00009)
    • R. Hilfer (ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore (2000). MR1890104 (2002j:00009)
    • (2000) Applications of Fractional Calculus in Physics
  • 15
    • 84966226768 scopus 로고
    • Semidiscretization in time for parabolic problems
    • MR0528047 (80f:65101)
    • M. N. Le Roux, Semidiscretization in time for parabolic problems, Math. Comp. 33 (1979) 919-931. MR0528047 (80f:65101)
    • (1979) Math. Comp. , vol.33 , pp. 919-931
    • Le Roux, M.N.1
  • 16
    • 0003900418 scopus 로고
    • Finite-element methods for a strongly damped wave equation
    • MR1089551 (92d:65164)
    • S. Larsson, V. Thomée, and L. B. Wahlbin, Finite-element methods for a strongly damped wave equation, IMA J. Numer. Anal. 11 (1991) 115-142. MR1089551 (92d:65164)
    • (1991) IMA J. Numer. Anal. , vol.11 , pp. 115-142
    • Larsson, S.1    Thomée, V.2    Wahlbin, L.B.3
  • 17
    • 0025383598 scopus 로고
    • A difference scheme for a nonlinear partial integrodifferential equation
    • MR1034918 (91e:65160)
    • J.C. López-Marcos, A difference scheme for a nonlinear partial integrodifferential equation, SIAM J. Numer. Anal. 27 (1990) 20-31. MR1034918 (91e:65160)
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 20-31
    • López-Marcos, J.C.1
  • 18
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • MR0838249 (87f:26006)
    • Ch. Lubich, Discretized fractional calculus, SIAM J. Math. Anal. 17 (1986) 704-719. MR0838249 (87f:26006)
    • (1986) SIAM J. Math. Anal. , vol.17 , pp. 704-719
    • Lubich, Ch.1
  • 19
    • 84966227123 scopus 로고
    • Fractional linear multistep methods for Abel-Volterra integral equations of the second kind
    • MR0804935 (86j:65181)
    • Ch. Lubich, Fractional linear multistep methods for Abel-Volterra integral equations of the second kind, Math. Comput. 45 (1985) 463-469. MR0804935 (86j:65181)
    • (1985) Math. Comput. , vol.45 , pp. 463-469
    • Lubich, Ch.1
  • 20
    • 0039541958 scopus 로고
    • On the numerical solution of Volterra equations with unbounded nonlinearity
    • MR0831243 (87k:65154)
    • Ch. Lubich, On the numerical solution of Volterra equations with unbounded nonlinearity, J. Integral Equations 10, Suppl. (1985) 175-183. MR0831243 (87k:65154)
    • (1985) J. Integral Equations , vol.10 , Issue.SUPPL. , pp. 175-183
    • Lubich, Ch.1
  • 21
    • 34250092484 scopus 로고
    • Convolution quadrature and discretized operational calculus. I
    • MR0923707 (89g:65018)
    • Ch. Lubich, Convolution quadrature and discretized operational calculus. I, Numer. Math. 52 (1988) 129-145. MR0923707 (89g:65018)
    • (1988) Numer. Math. , vol.52 , pp. 129-145
    • Lubich, Ch.1
  • 22
    • 8144220216 scopus 로고    scopus 로고
    • Convolution quadrature revisited
    • MR2106013 (2005f:65175)
    • Ch. Lubich, Convolution quadrature revisited, BIT 44 (2004) 503-514. MR2106013 (2005f:65175)
    • (2004) BIT , vol.44 , pp. 503-514
    • Lubich, Ch.1
  • 23
    • 0037252875 scopus 로고    scopus 로고
    • Fast convolution for nonreflecting boundary conditions
    • MR1924419 (2003h:44007)
    • Ch. Lubich and A. Schädle, Fast convolution for nonreflecting boundary conditions, SIAM J. Sci. Comp. 24 (2002), 161-182. MR1924419 (2003h:44007)
    • (2002) SIAM J. Sci. Comp. , vol.24 , pp. 161-182
    • Lubich, Ch.1    Schädle, A.2
  • 24
    • 0030364596 scopus 로고    scopus 로고
    • Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
    • MR1322891 (96d:65207)
    • Ch. Lubich, I.H. Sloan, V. Thomée, Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term, Math. Comp. 65 (1996), 1-17. MR1322891 (96d:65207)
    • (1996) Math. Comp. , vol.65 , pp. 1-17
    • Lubich, Ch.1    Sloan, I.H.2    Thomée, V.3
  • 25
    • 0035562778 scopus 로고    scopus 로고
    • Fractional diffusive waves
    • MR1881799 (2002k:76121)
    • F. Mainardi and P. Paradisi, Fractional diffusive waves, J. Comput. Acoustics 9 (2001) 1417-1436. MR1881799 (2002k:76121)
    • (2001) J. Comput. Acoustics , vol.9 , pp. 1417-1436
    • Mainardi, F.1    Paradisi, P.2
  • 26
    • 0001797959 scopus 로고
    • Numerical solution of an evolution equation with a positive-type memory term
    • MR1225703 (94e:65094)
    • W. McLean and V. Thomeé, Numerical solution of an evolution equation with a positive-type memory term, J. Austral. Math. Soc. Ser. 35 (1993) 23-70. MR1225703 (94e:65094)
    • (1993) J. Austral. Math. Soc. Ser. , vol.35 , pp. 23-70
    • McLean, W.1    Thomeé, V.2
  • 27
    • 0030123212 scopus 로고    scopus 로고
    • Discretizations with variable time steps of an evolution equation with a positive-type memory term
    • MR1391611 (97b:65073)
    • W. McLean, V. Thomeé, and L. Wahlbin, Discretizations with variable time steps of an evolution equation with a positive-type memory term, J. Comput. Appl. Math. (1996) 49-69. MR1391611 (97b:65073)
    • (1996) J. Comput. Appl. Math. , pp. 49-69
    • McLean, W.1    Thomeé, V.2    Wahlbin, L.3
  • 28
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • MR1809268 (2001k:82082)
    • R. Metzler and J. Klafter, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Physics Reports 339 (2000) 1-77. MR1809268 (2001k:82082)
    • (2000) Physics Reports , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 29
    • 0034257243 scopus 로고    scopus 로고
    • Accelerating Brownian motion: A fractional dynamics approach to fast diffusion
    • R. Metzler and J. Klafter, Accelerating Brownian motion: a fractional dynamics approach to fast diffusion, Europhys. Lett. 51 (2000) 492-498.
    • (2000) Europhys. Lett. , vol.51 , pp. 492-498
    • Metzler, R.1    Klafter, J.2
  • 34
    • 0002128448 scopus 로고
    • Fractional calculus
    • MR0447500 (56:5811)
    • B. Ross, Fractional Calculus, Math. Mag. 50 (1977) 115-122. MR0447500 (56:5811)
    • (1977) Math. Mag. , vol.50 , pp. 115-122
    • Ross, B.1
  • 35
    • 0001754759 scopus 로고
    • A numerical method for a partial integro-differential equation
    • MR0933727 (89d:65113)
    • J. M. Sanz-Serna, A numerical method for a partial integro-differential equation, SIAM J. Numer. Anal. 25 (1988) 319-327. MR0933727 (89d:65113)
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 319-327
    • Sanz-Serna, J.M.1
  • 36
    • 0012661804 scopus 로고
    • A finite difference scheme for partial integro-differential equations with a weakly singular kernel
    • MR1199854 (93h:65169)
    • T. Tang, A finite difference scheme for partial integro-differential equations with a weakly singular kernel, Appl. Numer. Math. 11 (1993) 309-319. MR1199854 (93h:65169)
    • (1993) Appl. Numer. Math. , vol.11 , pp. 309-319
    • Tang, T.1
  • 37
    • 1542766225 scopus 로고
    • A note on collocation methods for Volterra integro-differential equations with weakly singular kernels
    • MR1199031 (93k:65111)
    • T. Tang, A note on collocation methods for Volterra integro-differential equations with weakly singular kernels, IMA J. Numer. Anal. 13 (1993) 93-99. MR1199031 (93k:65111)
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 93-99
    • Tang, T.1


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