Research PapersNo Access

ON TWO-DIMENSIONAL WHOOPING COUGH DYNAMICS OF CONVECTION TYPE

SALEEM OBAIDAT

King Saud University, Mathematics Department, College of Science, P. O. Box 2455, Riyadh 11451, Saudi Arabia

https://doi.org/10.1142/S0219519412500935Cited by:0 (Source: Crossref)

Abstract

Analyzes has been carried out for the two-dimensional whooping cough model. The solution of the arising nonlinear initial/boundary value problem is computed by a homotopy analysis method (HAM). Convergence of the derived solution is highlighted. The plotted graphs show great confidence into the used methodology of solution.

Keywords:

AMSC: 92D25, 35L45, 35B35, 65N99

References

Piyawong W, Spatio-temporal numerical modeling of whooping cough dynamics, PhD Thesis, Brunel University 2001 . Google Scholar
S. Chinviriyasit and W. Chinviriyasit , Appl. Math. Appl. 216 , 395 ( 2010 ) . Google Scholar
Q. He et al. , J. Infect. Dis. 170 , 873 ( 1994 ) . Crossref, Web of Science, Google Scholar
M. J. Keeling and B. T. Grenfell , Science 275 , 65 ( 1997 ) . Crossref, Web of Science, Google Scholar
C. J. Ducan , S. R. Ducan and S. Scot , Proc. R. Soc. Lond. B. 263 , 445 ( 1996 ) . Crossref, Web of Science, Google Scholar
L. F. Olsen , G. L. Truty and W. M. Schaffer , Theor. Popul. Biol. 33 , 344 ( 1986 ) . Crossref, Web of Science, Google Scholar
Liao SJ, The proposed homotopy analysis techniques for the solution of nonlinear problems, PhD Dissertation, Shanghai Jiao Tong University, Shanghai, 1992 (in English) . Google Scholar
S. J. Liao , Beyond Perturbation: Introduction to the Homotopy Analysis Method ( Chapman and Hall/CRC , Florida , 2004 ) . Google Scholar
S. J. Liao, Appl. Math. Comput. 147(2), 499 (2004). Crossref, Web of Science, Google Scholar
S. J. Liao , Commun. Nonlinear. Sci. Numer. Simul. 14 , 983 ( 2009 ) . Crossref, Web of Science, Google Scholar
A. Bataineh , M. Noorani and I. Hashim , Comput. Math. Appl. 55 , 2913 ( 2008 ) . Crossref, Web of Science, Google Scholar
T. Hayat, M. Nawaz and S. Obaidat, Appl. Math. Mech. Engl. 32(3), 361 (2011). Crossref, Web of Science, Google Scholar
J. He , Chaos. Solitons. Fractals. 26 , 695 ( 2005 ) . Crossref, Web of Science, Google Scholar