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Volumn 81, Issue 5, 2011, Pages 1045-1056

On the use of matrix functions for fractional partial differential equations

Author keywords

Fractional differential equation; Krylov subspace; Matrix function; Rational approximation

Indexed keywords

FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL ORDER; KRYLOV SUBSPACE; MATRIX FUNCTIONS; NUMERICAL EXPERIMENTS; QUADRATURE RULES; RATIONAL APPROXIMATIONS;

EID: 78751643802     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2010.10.009     Document Type: Article
Times cited : (60)

References (37)
  • 1
    • 0009626343 scopus 로고
    • A propos d'une note de M. Pierre Humbert
    • R.P. Agarwal A propos d'une note de M. Pierre Humbert C. R. Acad. Sci. Paris 236 1953 2031 2032
    • (1953) C. R. Acad. Sci. Paris , vol.236 , pp. 2031-2032
    • Agarwal, R.P.1
  • 2
    • 0036650559 scopus 로고    scopus 로고
    • Solution for a fractional diffusion-wave equation defined in a bounded domain
    • O.P. Agrawal Solution for a fractional diffusion-wave equation defined in a bounded domain Nonlinear Dyn. 29 1-4 2002 145 155
    • (2002) Nonlinear Dyn. , vol.29 , Issue.14 , pp. 145-155
    • Agrawal, O.P.1
  • 3
    • 0034032484 scopus 로고    scopus 로고
    • Application of a fractional advection-dispersion equation
    • D.A. Benson, S.W. Wheatcraft, and M.M. Meerschaert Application of a fractional advection-dispersion equation Water Resour. Res. 36 6 2000 1403 1412
    • (2000) Water Resour. Res. , vol.36 , Issue.6 , pp. 1403-1412
    • Benson, D.A.1    Wheatcraft, S.W.2    Meerschaert, M.M.3
  • 4
    • 34250386323 scopus 로고
    • Rationale Tschebyscheff-Approximation über unbeschränkten Intervallen
    • H.-P. Blatt Rationale Tschebyscheff-Approximation über unbeschränkten Intervallen Numer. Math. 27 2 1976/1977 179 190
    • (1976) Numer. Math. , vol.27 , Issue.2 , pp. 179-190
    • Blatt, H.-P.1
  • 5
    • 51749116733 scopus 로고    scopus 로고
    • Finite difference approximations for the fractional Fokker-Planck equation
    • S. Chen, F. Liu, P. Zhuang, and V. Anh Finite difference approximations for the fractional Fokker-Planck equation Appl. Math. Model. 33 2009 256 273
    • (2009) Appl. Math. Model. , vol.33 , pp. 256-273
    • Chen, S.1    Liu, F.2    Zhuang, P.3    Anh, V.4
  • 6
    • 1842865578 scopus 로고    scopus 로고
    • A Schur-Parlett algorithm for computing matrix functions
    • P.I. Davies, and N.J. Higham A Schur-Parlett algorithm for computing matrix functions SIAM J. Matrix Anal. Appl. 25 2 2003 464 485 (electronic)
    • (2003) SIAM J. Matrix Anal. Appl. , vol.25 , Issue.2 , pp. 464-485
    • Davies, P.I.1    Higham, N.J.2
  • 7
    • 36149001762 scopus 로고    scopus 로고
    • Numerical algorithm for the time fractional Fokker-Planck equation
    • W. Deng Numerical algorithm for the time fractional Fokker-Planck equation J. Comput. Phys. 227 2007 1510 1522
    • (2007) J. Comput. Phys. , vol.227 , pp. 1510-1522
    • Deng, W.1
  • 8
    • 4043121080 scopus 로고    scopus 로고
    • Detailed error analysis for a fractional Adams method
    • K. Diethelm, N.J. Ford, and A.D. Freed Detailed error analysis for a fractional Adams method Numer. Algorithms 36 1 2004 31 52
    • (2004) Numer. Algorithms , vol.36 , Issue.1 , pp. 31-52
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 9
    • 43449090362 scopus 로고    scopus 로고
    • Space-time fractional Schrödinger equation with time-independent potentials
    • J. Dong, and M. Xu Space-time fractional Schrödinger equation with time-independent potentials J. Math. Anal. Appl. 344 2008 1005 1017
    • (2008) J. Math. Anal. Appl. , vol.344 , pp. 1005-1017
    • Dong, J.1    Xu, M.2
  • 11
    • 56949091229 scopus 로고    scopus 로고
    • Fractional Adams-Moulton methods
    • L. Galeone, and R. Garrappa Fractional Adams-Moulton methods Math. Comput. Simulat. 79 4 2008 1358 1367
    • (2008) Math. Comput. Simulat. , vol.79 , Issue.4 , pp. 1358-1367
    • Galeone, L.1    Garrappa, R.2
  • 12
    • 0001287486 scopus 로고
    • Fast numerical solution of nonlinear Volterra convolution equations
    • E. Hairer, C. Lubich, and M. Schlichte Fast numerical solution of nonlinear Volterra convolution equations SIAM J. Sci. Statist. Comput. 6 3 1985 532 541
    • (1985) SIAM J. Sci. Statist. Comput. , vol.6 , Issue.3 , pp. 532-541
    • Hairer, E.1    Lubich, C.2    Schlichte, M.3
  • 15
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov subspace approximations to the matrix exponential operator
    • M. Hochbruck, and C. Lubich On Krylov subspace approximations to the matrix exponential operator SIAM J. Numer. Anal. 34 5 1997 1911 1925
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.5 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, C.2
  • 17
    • 1542425102 scopus 로고    scopus 로고
    • Numerical solution of the space fractional Fokker-Planck equation
    • F. Liu, V. Anh, and I. Turner Numerical solution of the space fractional Fokker-Planck equation J. Comput. Appl. Math. 166 1 2004 209 219
    • (2004) J. Comput. Appl. Math. , vol.166 , Issue.1 , pp. 209-219
    • Liu, F.1    Anh, V.2    Turner, I.3
  • 18
    • 33845347760 scopus 로고    scopus 로고
    • Analysis of projection methods for rational function approximation to the matrix exponential
    • L. Lopez, and V. Simoncini Analysis of projection methods for rational function approximation to the matrix exponential SIAM J. Numer. Anal. 44 2 2006 613 635
    • (2006) SIAM J. Numer. Anal. , vol.44 , Issue.2 , pp. 613-635
    • Lopez, L.1    Simoncini, V.2
  • 19
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • C. Lubich 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
  • 20
    • 0005493050 scopus 로고
    • Asymptotics and super asymptotics for best rational approximation error norms to the exponential function (the "1/9" problem) by the Carathéodory-Fejér method
    • A.P. Magnus Asymptotics and super asymptotics for best rational approximation error norms to the exponential function (the "1/9" problem) by the Carathéodory-Fejér method Nonlinear Numer. Methods Ration. Approx. II 296 1994 173 185
    • (1994) Nonlinear Numer. Methods Ration. Approx. II , vol.296 , pp. 173-185
    • Magnus, A.P.1
  • 21
    • 4444368867 scopus 로고    scopus 로고
    • Finite difference approximations for fractional advection-dispersion flow equations
    • M.M. Meerschaert, and C. Tadjeran Finite difference approximations for fractional advection-dispersion flow equations J. Comput. Appl. Math. 172 1 2004 65 77
    • (2004) J. Comput. Appl. Math. , vol.172 , Issue.1 , pp. 65-77
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 23
    • 8144228833 scopus 로고    scopus 로고
    • RD-rational approximations of the matrix exponential
    • I. Moret, and P. Novati RD-rational approximations of the matrix exponential BIT 44 3 2004 595 615
    • (2004) BIT , vol.44 , Issue.3 , pp. 595-615
    • Moret, I.1    Novati, P.2
  • 25
    • 36549063424 scopus 로고    scopus 로고
    • A generalized differential transform method for linear partial differential equations of fractional order
    • DOI 10.1016/j.aml.2007.02.022, PII S0893965907001279
    • Z. Odibat, and S. Momani A generalized differential transform method for linear partial differential equations of fractional order Appl. Math. Lett. 21 2008 194 199 (Pubitemid 350181314)
    • (2008) Applied Mathematics Letters , vol.21 , Issue.2 , pp. 194-199
    • Odibat, Z.1    Momani, S.2
  • 29
    • 49749108595 scopus 로고    scopus 로고
    • Acceleration techniques for approximating the matrix exponential
    • M. Popolizio, and V. Simoncini Acceleration techniques for approximating the matrix exponential SIAM J. Matrix Analysis Appl. 30 2 2008 657 683
    • (2008) SIAM J. Matrix Analysis Appl. , vol.30 , Issue.2 , pp. 657-683
    • Popolizio, M.1    Simoncini, V.2
  • 30
    • 58149333483 scopus 로고    scopus 로고
    • Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals
    • T. Schmelzer, and L.N. Trefethen Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals ETNA 29 2007 1 18
    • (2007) ETNA , vol.29 , pp. 1-18
    • Schmelzer, T.1    Trefethen, L.N.2
  • 31
    • 0001553919 scopus 로고
    • Fractional diffusion and wave equations
    • W.R. Schneider, and W. Wyss Fractional diffusion and wave equations J. Math. Phys. 30 1 1989 134 144
    • (1989) J. Math. Phys. , vol.30 , Issue.1 , pp. 134-144
    • Schneider, W.R.1    Wyss, W.2
  • 32
    • 0007235470 scopus 로고
    • Rational Chebyshev approximation on the unit disk
    • L.N. Trefethen Rational Chebyshev approximation on the unit disk Numer. Math. 37 2 1981 297 320
    • (1981) Numer. Math. , vol.37 , Issue.2 , pp. 297-320
    • Trefethen, L.N.1
  • 33
    • 0041728453 scopus 로고
    • Circularity of the error curve and sharpness of the CF method in complex Chebyshev approximation
    • L.N. Trefethen Circularity of the error curve and sharpness of the CF method in complex Chebyshev approximation SIAM J. Numer. Anal. 20 6 1983 1258 1263
    • (1983) SIAM J. Numer. Anal. , vol.20 , Issue.6 , pp. 1258-1263
    • Trefethen, L.N.1
  • 34
    • 0011544931 scopus 로고
    • The Carathéodory-Fejér method for real rational approximation
    • L.N. Trefethen, and M.H. Gutknecht The Carathéodory-Fejér method for real rational approximation SIAM J. Numer. Anal. 20 2 1983 420 436
    • (1983) SIAM J. Numer. Anal. , vol.20 , Issue.2 , pp. 420-436
    • Trefethen, L.N.1    Gutknecht, M.H.2
  • 35
    • 33749016203 scopus 로고    scopus 로고
    • Talbot quadratures and rational approximations
    • L.N. Trefethen, J.A.C. Weideman, and T. Schmelzer Talbot quadratures and rational approximations BIT 46 3 2006 653 670
    • (2006) BIT , vol.46 , Issue.3 , pp. 653-670
    • Trefethen, L.N.1    Weideman, J.A.C.2    Schmelzer, T.3
  • 36
    • 33646928736 scopus 로고    scopus 로고
    • Preconditioning Lanczos approximations to the matrix exponential
    • J. van den Eshof, and M. Hochbruck Preconditioning Lanczos approximations to the matrix exponential SIAM J. Sci. Comput. 27 4 2006 1438 1457 (electronic)
    • (2006) SIAM J. Sci. Comput. , vol.27 , Issue.4 , pp. 1438-1457
    • Van Den Eshof, J.1    Hochbruck, M.2
  • 37
    • 34548162562 scopus 로고    scopus 로고
    • Parabolic and hyperbolic contours for computing the Bromwich integral
    • J.A.C. Weideman, and L.N. Trefethen Parabolic and hyperbolic contours for computing the Bromwich integral Math. Comput. 76 259 2007 1341 1356 (electronic)
    • (2007) Math. Comput. , vol.76 , Issue.259 , pp. 1341-1356
    • Weideman, J.A.C.1    Trefethen, L.N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.