메뉴 건너뛰기




Volumn 61, Issue 1, 2011, Pages 30-43

An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis

Author keywords

Caputo derivative; Fractional differential equations; Operational approach to the Tau method; Tau method

Indexed keywords

CAPUTO DERIVATIVES; CAPUTO SENSE; CONVERGENCE ANALYSIS; EXPONENTIAL RATES; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; L2-NORM; MATRIX VECTOR MULTIPLICATION; NUMERICAL APPROACHES; NUMERICAL RESULTS; NUMERICAL SOLUTION; ORTHOGONAL POLYNOMIAL; RATE OF CONVERGENCE; TAU METHOD; THEORETICAL PREDICTION;

EID: 78649445937     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.10.027     Document Type: Article
Times cited : (97)

References (30)
  • 1
    • 0032324531 scopus 로고    scopus 로고
    • Application of fractional calculus to viscoelastic behaviour modelling and to the physical ageing phenomenon in glassy amorphous polymers
    • M. Alcoutlabi, and J.J. Martinez-Vega Application of fractional calculus to viscoelastic behaviour modelling and to the physical ageing phenomenon in glassy amorphous polymers Polymer 39 1998 6269 6277
    • (1998) Polymer , vol.39 , pp. 6269-6277
    • Alcoutlabi, M.1    Martinez-Vega, J.J.2
  • 2
    • 0007042083 scopus 로고    scopus 로고
    • Nonlinear oscillation with fractional derivative and its applications
    • Dalian, China
    • J.H. He, Nonlinear oscillation with fractional derivative and its applications, in: International Conference on Vibrating Engineering, vol. 98, Dalian, China, 1998, pp. 288291.
    • (1998) International Conference on Vibrating Engineering , vol.98 , pp. 288-291
    • He, J.H.1
  • 3
    • 0347763940 scopus 로고    scopus 로고
    • Some applications of nonlinear fractional differential equations and their approximations
    • J.H. He Some applications of nonlinear fractional differential equations and their approximations Bull. Sci. Technol. 15 2 1999 86 90
    • (1999) Bull. Sci. Technol. , vol.15 , Issue.2 , pp. 86-90
    • He, J.H.1
  • 4
    • 35349007529 scopus 로고    scopus 로고
    • Generalized differential transform method for solving a space and time-fractional diffusion-wave equation
    • S. Momani, Z. Odibat, and V.S. Erturk Generalized differential transform method for solving a space and time-fractional diffusion-wave equation Phys. Lett. A 370 56 2007 379 387
    • (2007) Phys. Lett. A , vol.370 , Issue.56 , pp. 379-387
    • Momani, S.1    Odibat, Z.2    Erturk, V.S.3
  • 5
    • 34250647432 scopus 로고    scopus 로고
    • An approximation solution of a nonlinear equation with RiemannLiouville's fractional derivatives by He's variational iteration method
    • S. Abbasbandy An approximation solution of a nonlinear equation with RiemannLiouville's fractional derivatives by He's variational iteration method J. Comput. Appl. Math. 207 2007 53 58
    • (2007) J. Comput. Appl. Math. , vol.207 , pp. 53-58
    • Abbasbandy, S.1
  • 6
    • 35349007940 scopus 로고    scopus 로고
    • Numerical studies for a multi-order fractional differential equation
    • N.H. Sweilam, M.M. Khader, and R.F. Al-Bar Numerical studies for a multi-order fractional differential equation Phys. Lett. A 371 12 2007 26 33
    • (2007) Phys. Lett. A , vol.371 , Issue.12 , pp. 26-33
    • Sweilam, N.H.1    Khader, M.M.2    Al-Bar, R.F.3
  • 7
    • 33748901201 scopus 로고    scopus 로고
    • The adomian decomposition method for solving partial differential equations of fractal order in finite domains
    • A.M.A. El-Sayed, and M. Gaber The adomian decomposition method for solving partial differential equations of fractal order in finite domains Phys. Lett. A 359 3 2006 175 182
    • (2006) Phys. Lett. A , vol.359 , Issue.3 , pp. 175-182
    • El-Sayed, A.M.A.1    Gaber, M.2
  • 8
    • 33746218471 scopus 로고    scopus 로고
    • Solving a system of nonlinear fractional differential equations using Adomian decomposition
    • DOI 10.1016/j.cam.2005.10.017, PII S0377042705006278
    • H. Jafari, and V. Daftardar-Gejji Solving a system of nonlinear fractional differential equations using adomian decomposition J. Comput. Appl. Math. 196 2 2006 644 651 (Pubitemid 44093887)
    • (2006) Journal of Computational and Applied Mathematics , vol.196 , Issue.2 , pp. 644-651
    • Jafari, H.1    Daftardar-Gejji, V.2
  • 9
    • 0043044718 scopus 로고    scopus 로고
    • Numerical solution of fractional order differential equations by extrapolation
    • K. Diethelm, and G. Walz Numerical solution of fractional order differential equations by extrapolation Numer. Algorithms 16 34 1997 231 253 (Pubitemid 127429647)
    • (1997) Numerical Algorithms , vol.16 , Issue.3-4 , pp. 231-253
    • Diethelm, K.1    Walz, G.2
  • 10
    • 34247395044 scopus 로고    scopus 로고
    • Homotopy perturbation method for nonlinear partial differential equations of fractional order
    • S. Momani, and Z. Odibat Homotopy perturbation method for nonlinear partial differential equations of fractional order Phys. Lett. A 365 2007 345 350
    • (2007) Phys. Lett. A , vol.365 , pp. 345-350
    • Momani, S.1    Odibat, Z.2
  • 11
    • 34250215244 scopus 로고    scopus 로고
    • Solution of fractional differential equations by using differential transform method
    • A. Arikoglu, and I. Ozkol Solution of fractional differential equations by using differential transform method Chaos Solitons Fractals 34 5 2007 1473 1481
    • (2007) Chaos Solitons Fractals , vol.34 , Issue.5 , pp. 1473-1481
    • Arikoglu, A.1    Ozkol, I.2
  • 13
    • 0019659830 scopus 로고
    • An operational approach to the Tau method for the numerical solution of nonlinear differential equations
    • E.L. Ortiz, and H. Samara An operational approach to the Tau method for the numerical solution of nonlinear differential equations Computing 27 1 1981 15 25 (Pubitemid 12519953)
    • (1981) Computing (Vienna/New York) , vol.27 , Issue.1 , pp. 15-25
    • Ortiz, E.L.1    Samara, H.2
  • 14
    • 0020905495 scopus 로고
    • Numerical solution of differential eigenvalue problems with an operational approach to the Tau method
    • E.L. Ortiz, and H. Samara Numerical solution of differential eigenvalue problems with an operational approach to the Tau method Computing 31 2 1983 95 103 (Pubitemid 14472687)
    • (1983) Computing (Vienna/New York) , vol.31 , Issue.2 , pp. 95-103
    • Ortiz, E.L.1    Samara, H.2
  • 15
    • 4244163123 scopus 로고
    • Numerical solution of nonlinear partial differential equations with the Tau method
    • Proceedings of the International Conference on Computational and Applied Mathematics, Leuven, 1984
    • E.L. Ortiz, and K.S. Pun Numerical solution of nonlinear partial differential equations with the Tau method Proceedings of the International Conference on Computational and Applied Mathematics Leuven, 1984 J. Comput. Appl. Math. 1213 1985 511 516
    • (1985) J. Comput. Appl. Math. , vol.1213 , pp. 511-516
    • Ortiz, E.L.1    Pun, K.S.2
  • 16
    • 0031537729 scopus 로고    scopus 로고
    • Iterated solutions of linear operator equations with the Tau method
    • M.K. El-Daou, and H.G. Khajah Iterated solutions of linear operator equations with the Tau method Math. Comp. 66 217 1997 207 213
    • (1997) Math. Comp. , vol.66 , Issue.217 , pp. 207-213
    • El-Daou, M.K.1    Khajah, H.G.2
  • 17
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent. Part II
    • M. Caputo Linear models of dissipation whose Q is almost frequency independent. Part II Geophys. J. R. Astron. Soc. 13 1967 529 539
    • (1967) Geophys. J. R. Astron. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 21
  • 22
    • 0003258602 scopus 로고    scopus 로고
    • The generalized hardy operator with kernel and variable integral limits in Banach function spaces
    • A. Gogatishvill, and J. Lang The generalized hardy operator with kernel and variable integral limits in Banach function spaces J. Inequal. Appl. 4 1 1999 1 16
    • (1999) J. Inequal. Appl. , vol.4 , Issue.1 , pp. 1-16
    • Gogatishvill, A.1    Lang, J.2
  • 23
    • 77952816520 scopus 로고    scopus 로고
    • Convergence analysis of the Jacobi spectral collocation methods for Volterra integral equations with a weakly singular kernel
    • Y. Chen, and T. Tang Convergence analysis of the Jacobi spectral collocation methods for Volterra integral equations with a weakly singular kernel Math. Comp. 79 269 2010 147 167
    • (2010) Math. Comp. , vol.79 , Issue.269 , pp. 147-167
    • Chen, Y.1    Tang, T.2
  • 24
    • 0242447633 scopus 로고
    • Linear Operator Theory in Engineering and Science
    • second ed. Springer-Verlag New York, Berlin
    • A.W. Naylor, and G.R. Sell Linear Operator Theory in Engineering and Science second ed. Applied Mathematical Sciences vol. 40 1982 Springer-Verlag New York, Berlin
    • (1982) Applied Mathematical Sciences , vol.40
    • Naylor, A.W.1    Sell, G.R.2
  • 25
    • 61549094949 scopus 로고    scopus 로고
    • Generalized Jacobi polynomials/functions and their applications
    • Ben-Yu Guo, Jie Shen, and Li-Lian Wang Generalized Jacobi polynomials/functions and their applications Appl. Numer. Math. 59 5 2009 1011 1028
    • (2009) Appl. Numer. Math. , vol.59 , Issue.5 , pp. 1011-1028
    • Guo, B.-Y.1    Shen, J.2    Wang, L.-L.3
  • 27
    • 33748425302 scopus 로고    scopus 로고
    • Numerical comparison of methods for solving linear differential equations of fractional order
    • S. Momani, and Z. Odibat Numerical comparison of methods for solving linear differential equations of fractional order Chaos Solitons Fractals 31 5 2007 1248 1255
    • (2007) Chaos Solitons Fractals , vol.31 , Issue.5 , pp. 1248-1255
    • Momani, S.1    Odibat, Z.2
  • 28
    • 9744276851 scopus 로고    scopus 로고
    • Numerical methods for multi-term fractional (arbitrary) orders differential equations
    • A.E.M. El-Mesiry, A.M.A. El-Sayed, and H.A.A. El-Saka Numerical methods for multi-term fractional (arbitrary) orders differential equations Appl. Math. Comput. 160 3 2005 683 699
    • (2005) Appl. Math. Comput. , vol.160 , Issue.3 , pp. 683-699
    • El-Mesiry, A.E.M.1    El-Sayed, A.M.A.2    El-Saka, H.A.A.3
  • 29
    • 0028750042 scopus 로고
    • The ChebyshevLegendre method: Implementing Legendre methods on Chebyshev points
    • W. Sun Don, and D. Gottlieb The ChebyshevLegendre method: implementing Legendre methods on Chebyshev points SIAM J. Numer. Anal. 31 6 1994 1519 1534 (English summary)
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.6 , pp. 1519-1534
    • Sun Don, W.1    Gottlieb, D.2
  • 30
    • 0000944835 scopus 로고
    • A fast algorithm for the evaluation of Legendre expansions
    • B.K. Alpert, and V. Rokhlin A fast algorithm for the evaluation of Legendre expansions SIAM J. Sci. Stat. Comput. 12 1 1991 158 179
    • (1991) SIAM J. Sci. Stat. Comput. , vol.12 , Issue.1 , pp. 158-179
    • Alpert, B.K.1    Rokhlin, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.