A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

Central European Journal of Physics

Volumn 12, Issue 2, 2014, Pages 111-122

  Doha, Eid H ^a   Bhrawy, Ali H ^b,c   Abdelkawy, Mohamed A ^c   Hafez, Ramy M ^d  

^a CAIRO UNIVERSITY   (Egypt)

^b KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^c BENI SUEF UNIVERSITY   (Egypt)

^d Modern Academy   (Egypt)

Author keywords

implicit Runge Kutta Nystr m scheme; Jacobi quadrature rule; nonlinear coupled viscous Burgers' equation; pseudospectral scheme

Indexed keywords

EID: 84893984926     PISSN: 18951082     EISSN: 16443608     Source Type: Journal    
DOI: 10.2478/s11534-014-0429-z     Document Type: Article

References (38)

1. S. E. Esipov, Phys. Rev. E 52, 3711 (1995).
2. J. D. Cole, Q. Appl. Math. 9, 225 (1951).
3. J. Burgers, A mathematical model illustrating the theory of turbulence, Advances in Applied Mechanics (Academic Press, New York, 1948).
4. M. A. Abdou, A. A. Soliman, J. Comput. Appl. Math. 181, 245 (2005).
5. H. Aminikhah, Appl. Math. Model. 37, 5979 (2013).
6. A. H. Khater, R. S. Temsah, M. M. Hassan, J. Comput. Appl. Math. 222, 33 (2008).
7. D. Kaya, IJMMS 27, 675 (2001).
8. I. Kucuk, I. Sadek, Appl. Math. Comput. 210, 126 (2009).
9. M. T. Darvishi, S. Kheybari, F. Khani, Commun. Nonlinear Sci. Numer. Simul. 13, 2091 (2008).
10. M. Javidi, A. Golbabai, J. Math. Anal. Appl. 333, 1119 (2007).
11. E. Tohidi, A. H. Bhrawy, K. Erfani, Appl. Math. Model. 37, 4283 (2013).
12. Y. -Y. Kwan, Appl. Numer. Math. 59, 170 (2009).
13. F. Chen, J. Shen, J. Comput. Phys. 231, 5016 (2012).
14. F. Ghoreishi, S. Yazdani, Comput. Math. Appl. 61, 30 (2011).
15. E. H. Doha, A. H. Bhrawy, R. M. Hafez, Commun. Nonlinear Sci. Numer. Simul. 17, 3802 (2012).
16. T. Kattelans, W. Heinrichs, J. Comput. Phys. 228, 4649 (2009).
17. B. W. Li, S. Tian, Y. S. Sun, Z. M. Hu, J. Comput. Phys. 229, 1198 (2010).
18. K. Parand, M. Shahini, M. Dehghan, J. Comput. Phys. 228, 8830 (2009).
19. M. Dehghan, F. F. Izadi, Math. Comput. Model. 53, 1865 (2011).
20. A. H. Bhrawy, Appl. Math. Comput. 222, 255 (2013).
21. Y. Ordokhani, M. Razzaghi, Appl. Math. Lett. 21, 4 (2008).
22. K. Zhang, J. Li, H. Song, Appl. Math. Comput. 218, 10848 (2012).
23. Y. Jiang, J. Ma, J. Comput. Appl. Math. 244, 115 (2013).
24. S. Yüzbasi, M. Sezer, B. Kemanci, Appl. Math. Model. 37, 2086 (2013).
25. A. H. Bhrawy, M. M. Tharwat, A. Yildirim, Appl. Math. Model. 37, 4245 (2013).
26. C. Canuto, M. Y. Hussaini, A. Quarteroni, T. A. Zang, Spectral Methods: Fundamentals in Single Domains (Springer-Verlag, New York, 2006).
27. A. H. Bhrawy, A. S. Alofi, Commun. Nonlinear Sci. Numer. Simul. 17, 62 (2012).
28. B. Bialecki, A. Karageorghis, J. Comput. Phys. 227, 8588 (2008).
29. S. Esmaeili, M. Shamsi, Y. Luchko, Comput. Math. Appl. 62, 918 (2011).
30. E. H. Doha, A. H. Bhrawy, R. M. Hafez, Math. Comput. Model. 53, 1820 (2011).
31. D. Gottlieb, C. -W. Shu, SIAM Rev. 29, 644 (1997).
32. D. Tchiotsop, D. Wolf, V. Louis-Dorr, R. Husson, ECG data compression using Jacobi polynomials, Proceedings of the 29th Annual International Conference of the IEEE EMBS, August 23-26, 2007, Lyon, France (Engineering in Medicine and Biology Society, France, 2007) 1863.
33. E. H. Doha, A. H. Bhrawy, Numer. Meth. Part. D. E. 25, 712 (2009).
34. M. El-Kady, J. Korean Math. Soc. 49, 99 (2012).
35. G. Szegö, Orthogonal Polynomials, Colloquium Publications, XXIII (American Mathematical Society, Rhode Islands, 1939).
36. R. C. Mittal, G. Arora, Commun. Nonlinear Sci. Numer. Simul. 16, 1304 (2011).
37. A. Rashid, A. I. B. Ismail, Comput. Methods App. Math. 9, 412 (2009).
38. R. A. van Gorder, Acta Mech. 216, 345 (2011).