메뉴 건너뛰기




Volumn 14, Issue 3, 2011, Pages 475-490

An efficient parallel algorithm for the numerical solution of fractional differential equations

Author keywords

Adams Bashforth Moulton method; fractional differential equation; numerical solution; parallel algorithm

Indexed keywords


EID: 80051704994     PISSN: 13110454     EISSN: 13142444     Source Type: Journal    
DOI: 10.2478/s13540-011-0029-1     Document Type: Article
Times cited : (88)

References (33)
  • 2
    • 79953881634 scopus 로고    scopus 로고
    • Comprehensive performance tracking with Vampir 7
    • M. S. Müller M. M. Resch A. Schulz W. E. Nagel (eds). Springer Berlin. 10.1007/978-3-642-11261-4-2
    • H. Brunst, D. Hackenberg, G. Juckeland and H. Rohling, Comprehensive performance tracking with Vampir 7. Tools for High Performance Computing 2009 (M. S. Müller, M. M. Resch, A. Schulz and W. E. Nagel, Eds.) Springer, Berlin (2010), 17-29.
    • (2010) Tools for High Performance Computing 2009 , pp. 17-29
    • Brunst, H.1    Hackenberg, D.2    Juckeland, G.3    Rohling, H.4
  • 3
    • 84957869022 scopus 로고    scopus 로고
    • Performance Optimization for Large Scale Computing: The Scalable VAMPIR Approach
    • Computational Science - ICCS 2001
    • H. Brunst, M. Winkler, W. E. Nagel and H.-C. Hoppe, Performance optimization for large scale computing: The scalable VAMPIR approach. Computational Science - ICCS 2001, Part II (au]V. N. Alexandrov, J. J. Dongarra, B. A. Juliano, R. S. Renner and C. J. K. Tan, Eds.), Springer, Berlin (2001), 751-760. (Pubitemid 33285639)
    • (2001) Computational Science - ICCS 2001 , Issue.2074 , pp. 751-760
    • Brunst, H.1    Winkler, M.2    Nagel, W.E.3    Hoppe, H.-C.4
  • 4
    • 0348158242 scopus 로고    scopus 로고
    • mE methods
    • 1035.65066 10.1007/s00607-003-0033-3
    • mE methods Computing 71 305 319 1035.65066 10.1007/s00607-003-0033-3
    • (2003) Computing , vol.71 , pp. 305-319
    • Diethelm, K.1
  • 7
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • DOI 10.1023/A:1016592219341, Fractional Order Calculus and Its Applications
    • K. Diethelm N.J. Ford A.D. Freed 2002 A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dynamics 29 3 22 1009.65049 10.1023/A:1016592219341 (Pubitemid 34945390)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 8
    • 4043121080 scopus 로고    scopus 로고
    • Detailed error analysis for a fractional Adams method
    • DOI 10.1023/B:NUMA.0000027736.85078.be
    • K. Diethelm N.J. Ford A.D. Freed 2004 Detailed error analysis for a fractional Adams method Numer. Algorithms 36 31 52 1055.65098 10.1023/B:NUMA.0000027736.85078.be (Pubitemid 39072748)
    • (2004) Numerical Algorithms , vol.36 , Issue.1 , pp. 31-52
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 9
    • 10644238068 scopus 로고    scopus 로고
    • Algorithms for the fractional calculus: A selection of numerical methods
    • DOI 10.1016/j.cma.2004.06.006, PII S0045782504002981
    • K. Diethelm N.J. Ford A.D. Freed Y. Luchko 2005 Algorithms for the fractional calculus: A selection of numerical methods Comput. Methods Appl. Mech. Eng. 194 743 773 1119.65352 10.1016/j.cma.2004.06.006 (Pubitemid 39660444)
    • (2005) Computer Methods in Applied Mechanics and Engineering , vol.194 , Issue.6-8 , pp. 743-773
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3    Luchko, Yu.4
  • 10
    • 33646341532 scopus 로고    scopus 로고
    • Comparison of numerical methods for fractional differential equations
    • DOI 10.3934/cpaa.2006.5.289
    • N.J. Ford J.A. Connolly 2006 Comparison of numerical methods for fractional differential equations Commun. Pure Appl. Anal. 5 289 307 1133.65115 10.3934/cpaa.2006.5.289 (Pubitemid 43671806)
    • (2006) Communications on Pure and Applied Analysis , vol.5 , Issue.2 , pp. 289-307
    • Ford, N.J.1    Connolly, J.A.2
  • 11
    • 0035625795 scopus 로고    scopus 로고
    • The numerical solution of fractional differential equations: Speed versus accuracy
    • N.J. Ford and A.C. Simpson, The numerical solution of fractional differential equations: Speed versus accuracy. Numer. Algorithms 26 (2001), 333-346.
    • (2001) Numer. Algorithms , vol.26 , pp. 333-346
    • Ford, N.J.1    Simpson, A.C.2
  • 14
    • 80051684093 scopus 로고    scopus 로고
    • GNS mbH, The Numerical Forming Simulation Software Package INDEED
    • GNS mbH, The Numerical Forming Simulation Software Package INDEED; http://www.gns-mbh.com/indeed.html
  • 15
    • 80051696936 scopus 로고    scopus 로고
    • GWT-TUD GmbH, Vampir Performance Optimization
    • GWT-TUD GmbH, Vampir Performance Optimization; http://www.vampir.eu
  • 19
    • 80051704367 scopus 로고    scopus 로고
    • Jülich Supercomputing Centre, SCALASCA - Scalable Performance Analysis of Large-Scale Applications
    • Jülich Supercomputing Centre, SCALASCA - Scalable Performance Analysis of Large-Scale Applications; http://www.scalasca.org
  • 20
    • 84889299911 scopus 로고    scopus 로고
    • R. Klages G. Radons I. M. Sokolov (eds). Wiley-VCH Weinheim
    • R. Klages, G. Radons and I. M. Sokolov (Eds.), Anomalous Transport: Foundations and Applications. Wiley-VCH, Weinheim (2008).
    • (2008) Anomalous Transport: Foundations and Applications
  • 22
    • 84962571892 scopus 로고
    • Runge-Kutta theory for Volterra and Abel integral equations of the second kind
    • 0538.65091 10.1090/S0025-5718-1983-0701626-6
    • C. Lubich 1983 Runge-Kutta theory for Volterra and Abel integral equations of the second kind Math. Comp. 41 87 102 0538.65091 10.1090/S0025-5718-1983-0701626-6
    • (1983) Math. Comp. , vol.41 , pp. 87-102
    • Lubich, C.1
  • 23
    • 84966227123 scopus 로고
    • Fractional linear multistep methods for Abel-Volterra integral equations of the second kind
    • 0584.65090 10.1090/S0025-5718-1985-0804935-7
    • C. Lubich 1985 Fractional linear multistep methods for Abel-Volterra integral equations of the second kind Math. Comp. 45 463 469 0584.65090 10.1090/S0025-5718-1985-0804935-7
    • (1985) Math. Comp. , vol.45 , pp. 463-469
    • Lubich, C.1
  • 25
    • 80051686338 scopus 로고    scopus 로고
    • Message Passing Interface Forum, MPI: A Message-Passing Interface Standard
    • Message Passing Interface Forum, MPI: A Message-Passing Interface Standard; http://www.mpi-forum.org/docs/docs.html
  • 26
    • 70349863847 scopus 로고    scopus 로고
    • Developing scalable applications with Vampir, VampirServer and VampirTrace
    • C. Bischof M. Bücker P. Gibbon G. R. Joubert T. Lippert B. Mohr F. Peters (eds). IOS Press Amsterdam
    • M. S. Müller, A. Knüpfer, M. Jurenz, M. Lieber, H. Brunst, H. Mix and W.E. Nagel, Developing scalable applications with Vampir, VampirServer and VampirTrace. Parallel Computing: Architectures, Algorithms and Applications (C. Bischof, M. Bücker, P. Gibbon, G. R. Joubert, T. Lippert, B. Mohr and F. Peters, Eds.), IOS Press, Amsterdam (2008), 637-644.
    • (2008) Parallel Computing: Architectures, Algorithms and Applications , pp. 637-644
    • Müller, M.S.1    Knüpfer, A.2    Jurenz, M.3    Lieber, M.4    Brunst, H.5    Mix, H.6    Nagel, W.E.7
  • 29
    • 80051688665 scopus 로고    scopus 로고
    • OpenMP Architecture Review Board, The OpenMP API Specification for Parallel Programming
    • OpenMP Architecture Review Board, The OpenMP API Specification for Parallel Programming; http://www.openmp.org
  • 32
    • 67650122083 scopus 로고    scopus 로고
    • Comments on stability analysis of a class of nonlinear fractional-order systems
    • 10.1109/TCSII.2009.2020944
    • M.S. Tavazoei 2009 Comments on stability analysis of a class of nonlinear fractional-order systems IEEE Trans. Circuits Systems II 56 519 520 10.1109/TCSII.2009.2020944
    • (2009) IEEE Trans. Circuits Systems II , vol.56 , pp. 519-520
    • Tavazoei, M.S.1
  • 33
    • 67649624652 scopus 로고    scopus 로고
    • Stability preservation analysis for frequency-based methods in numerical simulation of fractional-order systems
    • 10.1137/080715949
    • M.S. Tavazoei M. Haeri S. Bolouki M. Siami 2008 Stability preservation analysis for frequency-based methods in numerical simulation of fractional-order systems SIAM J. Numer. Anal. 47 321 328 10.1137/080715949
    • (2008) SIAM J. Numer. Anal. , vol.47 , pp. 321-328
    • Tavazoei, M.S.1    Haeri, M.2    Bolouki, S.3    Siami, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.