A spectral legendre-gauss-lobatto collocation method for a space-fractional advection diffusion equations with variable coefficients

Reports on Mathematical Physics

Volumn 72, Issue 2, 2013, Pages 219-233

  Bhrawy, A H ^a,b   Baleanu, D ^a,c,d  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^b Beni Suef University   (Egypt)

^c CANKAYA UNIVERSITY   (Turkey)

^d INSTITUTE OF SPACE SCIENCES   (Romania)

Author keywords

Implicit Runge Kutta method; Legendre Gauss Lobatto quadrature; Space fractional advection diffusion equation; Spectral method

Indexed keywords

EID: 84893626620     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(14)60015-X     Document Type: Article

References (31)

1. D. Baleanu, K. Diethelm, E. Scalas and J. J. Trujillo. Fractional calculus models and numerical methods, in: Series on Complexity, Nonlinearity and Chaos, World Scientific, Singapore, 2012.
2. F. Mainardi. Fractional calculus: some basic problems in continuum and statistical mechanics, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer, New York 1997.
3. A. M. Spasic and M. P. Lazarevic. J. Colloid Interface Sci. 282 (2005), 223.
4. A. A. Kilbas, H. M. Srivastava and J. J. Trujillo. Theory and Applications of Fractional Differential Equations, Elsevier, San Diego, 2006.
5. A. H. Bhrawy and M. A. Alghamdi. Bound. Value. Prob. 2012 (2012), 62.
6. E. H. Doha, A. H. Bhrawy and S. S. Ezz-Eldien. Appl. Math. Modell. 35 (2011), 5662.
7. X. Li and C. Xu. SIAM J. Numer. Anal. 45 (2009), 2108.
8. A. Saadatmandi and M. Dehghan. Comput. Math. Appl. 62 (2011), 1135.
9. A. Saadatmandi, M. Dehghan and M. R. Azizi. Commun. Nonlinear Sci. Numer. Simulat. 17 (2012), 4125.
10. R. Hilfer: (Ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
11. C. Celik and M. Duman. J. Comput. Phys. 231 (2012), 1743.
12. Chen J, F. Liu, I. Turner and V. Anh. ANZIAM J. 50 (2008), 45.
13. H. W. Choi, S. K. Chung and Y. J. Lee. Bull. Korean Math. Soc. 47 (2010), 1225.
14. F. Liu, P. Zhuang and K. Burrage. Comput. Math. Appl. 64 (2012), 2990.
15. C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang. Spectral Methods: Fundamentals in Single Domains, Springer, New York, 2006.
16. B.-Y. Guo and J.-P. Yan. Appl. Numer. Math. 59 (2009), 1386.
17. E. H. Doha, A. H. Bhrawy and S. S. Ezz-Eldien. Appl. Math. Model. 36 (2012), 4931.
18. A. H. Bhrawy and A. S. Alofi. Commun. Nonlinear. Sci. Numer. Simulat. 17 (2012), 62.
19. E. H. Doha, A. H. Bhrawy and R. M. Hafez. Commun. Nonlinear Sci. Numer. Simulat. 17 (2012), 3802.
20. E. H. Doha and A. H. Bhrawy. Appl. Numer. Math. 58 (2008), 1224.
21. Y. Zheng, C. Li and Z. Zhaoa. Comput. Math. Appl. 59 (2010), 1718.
22. L. Su, W. Wang and Q. Xu. Appl. Math. Comput. 216 (2010), 3329.
23. G. J. Fix and J. P. Roop. Comput. Math. Appl. 48 (2004), 1017.
24. E. Sousa Comput. Math. Appl. 62 (2011), 938.
25. C. Tadjeran, M. M. Meerschaert and H.-P. Scheffler J. Comput. Phys. 213 (2006), 205.
26. E. A. Abdel-Rehima and R. Gorenflo. J. Comput. Appl. Math. 222 (2008), 274.
27. H. Zhang, F. Liu and V. Anh. Appl. Math. Comput. 217 (2010), 2534.
28. B.-Y. Guo and L.-L. Wang. J. Appr. Theor. 128, (2004), 1-41.
29. A.H. Bhrawy, A.S. Alofi and S.S. Ezz-Eldien. Appl. Math. Lett. 24, 2146 (2011).
30. E. Sousa. Comput. Math. Appl. 64, 3141 (2012).
31. S.S. Ray, K.S. Chaudhuri, R.K. Bera. Appl. Math. Comput. 196, 294 (2008).