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Volumn 224, Issue , 2013, Pages 259-267

An efficient Chebyshev-tau method for solving the space fractional diffusion equations

Author keywords

Caputo derivative; Fractional diffusion equation; Operation matrix; Shifted Chebyshev polynomials; Tau method

Indexed keywords

CAPUTO DERIVATIVES; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFUSION EQUATION; INITIAL-BOUNDARY VALUE PROBLEMS; LINEAR ALGEBRAIC EQUATION; SHIFTED CHEBYSHEV POLYNOMIALS; SPACE-FRACTIONAL DIFFUSIONS; TAU METHOD;

EID: 84884805515     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2013.08.073     Document Type: Article
Times cited : (33)

References (15)
  • 2
    • 34248373867 scopus 로고    scopus 로고
    • Solving a multi-order fractional differential equation
    • V.D. Gejji, and H. Jafari Solving a multi-order fractional differential equation Appl. Math. Comput. 189 2007 541 548
    • (2007) Appl. Math. Comput. , vol.189 , pp. 541-548
    • Gejji, V.D.1    Jafari, H.2
  • 3
    • 3042776917 scopus 로고    scopus 로고
    • Fractional calculus in bio-engineering
    • R.L. Magin Fractional calculus in bio-engineering Crit. Rev. Biomed. Eng. 32 2004 1 104
    • (2004) Crit. Rev. Biomed. Eng. , vol.32 , pp. 1-104
    • Magin, R.L.1
  • 4
    • 30344464250 scopus 로고    scopus 로고
    • Application of variational iteration method to nonlinear differential equations of fractional order
    • Z. Odibat, and S. Momani Application of variational iteration method to nonlinear differential equations of fractional order Int. J. Nonlinear Sci. Numer. Simul. 7 2006 27 35
    • (2006) Int. J. Nonlinear Sci. Numer. Simul. , vol.7 , pp. 27-35
    • Odibat, Z.1    Momani, S.2
  • 5
    • 43949121726 scopus 로고    scopus 로고
    • The approximate and exact solutions of the space- and time-fractional Burger's equations with initial conditions by variational iteration method
    • M. Inc The approximate and exact solutions of the space- and time-fractional Burger's equations with initial conditions by variational iteration method J. Math. Anal. Appl. 345 2008 476 484
    • (2008) J. Math. Anal. Appl. , vol.345 , pp. 476-484
    • Inc, M.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 2007 26 33
    • (2007) Phys. Lett. A , vol.371 , pp. 26-33
    • Sweilam, N.H.1    Khader, M.M.2    Al-Bar, R.F.3
  • 7
    • 74249095517 scopus 로고    scopus 로고
    • A new operational matrix for solving fractional-order differential equations
    • A. Saadatmandi, and M. Dehghan A new operational matrix for solving fractional-order differential equations Comput. Math. Appl. 59 2010 1326 1336
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1326-1336
    • Saadatmandi, A.1    Dehghan, M.2
  • 8
    • 78651444144 scopus 로고    scopus 로고
    • On the numerical solutions for the fractional diffusion equation
    • M.M. Khader On the numerical solutions for the fractional diffusion equation Commun. Nonlinear Sci. Numer. Simul. 16 2011 2535 2542
    • (2011) Commun. Nonlinear Sci. Numer. Simul. , vol.16 , pp. 2535-2542
    • Khader, M.M.1
  • 9
    • 79960977916 scopus 로고    scopus 로고
    • A tau approach for solution of the space fractional diffusion equation
    • A. Saadatmandi, and M. Dehghan A tau approach for solution of the space fractional diffusion equation Comput. Math. Appl. 62 2011 1135 1142
    • (2011) Comput. Math. Appl. , vol.62 , pp. 1135-1142
    • Saadatmandi, A.1    Dehghan, M.2
  • 11
    • 0035251701 scopus 로고    scopus 로고
    • Frobenius-Chebyshev polynomial approximations with a priori error bounds for nonlinear initial value differential problems
    • DOI 10.1016/S0898-1221(00)00271-6
    • B. Chen, R. Garcia-Bolos, and L. Jodar Frobenius-Chebyshev polynomial approximations with a priori error bounds for nonlinear initial value differential problems Comput. Math. Appl. 41 2001 269 280 (Pubitemid 32168354)
    • (2001) Computers and Mathematics with Applications , vol.41 , Issue.3-4 , pp. 269-280
    • Chen, B.1    Garcia Bolos, R.2    Jodar, L.3
  • 12
    • 0038683230 scopus 로고    scopus 로고
    • The truncation error of the two-variable Chebyshev series expansions
    • B. Chen, R. Garcia-Bolos, and L. Jodar The truncation error of the two-variable Chebyshev series expansions Comput. Math. Appl. 45 2003 1647 1653
    • (2003) Comput. Math. Appl. , vol.45 , pp. 1647-1653
    • Chen, B.1    Garcia-Bolos, R.2    Jodar, L.3
  • 13
    • 0027335165 scopus 로고
    • Designing linear optimal regulators via Chebyshev polynomials
    • S.K. Wang, M.L. Nagurka, Designing linear optimal regulators via Chebyshev polynomials, in: American Control Conference, San Francisco, CA, 1993, pp. 2685-2689. (Pubitemid 23705429)
    • (1993) American Control Conference , pp. 2685-2689
    • Wang, S.-K.1    Nagurka, M.L.2
  • 14
    • 80052270048 scopus 로고    scopus 로고
    • A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order
    • E.H. Doha, A.H. Bhrawy, and S.S. Ezz-Eldien A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order Appl. Math. Model. 62 2011 2364 2373
    • (2011) Appl. Math. Model. , vol.62 , pp. 2364-2373
    • Doha, E.H.1    Bhrawy, A.H.2    Ezz-Eldien, S.S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.