zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Application of the homotopy analysis method for solving a model for HIV infection of CD4 + T-cells. (English) Zbl 1235.65095
Summary: The homotopy analysis method (HAM) is investigated to give an approximate solution of a model for HIV infection of CD4 + T-cells. This method allows for the solution of the governing differential equation to be calculated in the form of an infinite series with components which can be easily calculated. The HAM utilizes a simple method to adjust and control the convergence region of the infinite series solution by using an auxiliary parameter. The results obtained are presented, and six terms are sufficient to obtain an approximation solution that is very accurate.
MSC:
65L99Numerical methods for ODE
92D30Epidemiology
References:
[1]Perelson, A. S.: Modelling the interaction of the immune system with HIV, Mathematical and statistical approaches to AIDS epidemiology, 350 (1989) · Zbl 0683.92001
[2]Perelson, A. S.; Kirschner, D. E.; De Boer, R.: Dynamics of HIV infection of CD4+ T-cells, Mathematical biosciences 114, 81 (1993) · Zbl 0796.92016 · doi:10.1016/0025-5564(93)90043-A
[3]Culshaw, R. V.; Ruan, S.: A delay-differential equation model of HIV infection of CD4+ T-cells, Mathematical biosciences 165, 27-39 (2000) · Zbl 0981.92009 · doi:10.1016/S0025-5564(00)00006-7
[4]Wang, X.; Song, X.: Global stability and periodic solution of a model for HIV infection of CD4+ T-cells, Applied mathematics and computation 189, 1331-1340 (2007) · Zbl 1117.92040 · doi:10.1016/j.amc.2006.12.044
[5]Ongun, M. Y.: The Laplace Adomian decomposition method for solving a model for HIV infection of CD4+ T cells, Mathematical and computer modelling 53, 597-603 (2011) · Zbl 1217.65164 · doi:10.1016/j.mcm.2010.09.009
[6]M. Merdan, Homotopy perturbation method for solving a model for HIV infection of CD4+ T-cells, İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi Yil: 6 Sayi: 12 Güz 2007/2 s. pp. 39–52.
[7]Rashidi, M. M.; Pour, S. A. Mohimanian; Abbasbandy, S.: Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation, Communications in nonlinear science and numerical simulation 16, 1874-1889 (2011)
[8]Alomari, A. K.; Noorani, M. S. M.; Nazar, R.; Li, C. P.: Homotopy analysis method for solving fractional Lorenz system, Communications in nonlinear science and numerical simulation 15, 1864-1872 (2010) · Zbl 1222.65082 · doi:10.1016/j.cnsns.2009.08.005
[9]Bataineh, A. S.; Noorani, M. S. M.; Hashim, I.: Modified homotopy analysis method for solving systems of second-order BVPs, Communications in nonlinear science and numerical simulation 14, 430-442 (2009) · Zbl 1221.65196 · doi:10.1016/j.cnsns.2007.09.012
[10]Awawdeh, F.; Adawi, A.; Mustafa, Z.: Solutions of the SIR models of epidemics using HAM, Chaos, solitons and fractals 42, 3047-3052 (2009) · Zbl 1198.65132 · doi:10.1016/j.chaos.2009.04.012
[11]Abbasbandy, S.; Shirzadi, A.: A new application of the homotopy analysis method: solving the Sturm–Liouville problems, Communications in nonlinear science and numerical simulation 16, 112-126 (2011) · Zbl 1221.65189 · doi:10.1016/j.cnsns.2010.04.004
[12]Khan, M.; Munawar, S.; Abbasbandy, S.: Steady flow and heat transfer of a sisko fluid in annular pipe, International journal of heat and mass transfer 53, 1290-1297 (2010) · Zbl 1183.80034 · doi:10.1016/j.ijheatmasstransfer.2009.12.037
[13]Abbasbandy, S.; Babolian, E.; Ashtiani, M.: Numerical solution of the generalized Zakharov equation by homotopy analysis method, Communications in nonlinear science and numerical simulation 14, 4114-4121 (2009) · Zbl 1221.65269 · doi:10.1016/j.cnsns.2009.03.001
[14]Abbasbandy, S.; Magyari, E.; Shivanian, E.: The homotopy analysis method for multiple solutions of nonlinear boundary value problems, Communications in nonlinear science and numerical simulation 14, 3530-3536 (2009) · Zbl 1221.65170 · doi:10.1016/j.cnsns.2009.02.008
[15]Abbasbandy, S.; Hayat, T.: Solution of the MHD Falkner–Skan flow by homotopy analysis method, Communications in nonlinear science and numerical simulation 14, 3591-3598 (2009) · Zbl 1221.76133 · doi:10.1016/j.cnsns.2009.01.030
[16]Alomari, A. K.; Noorani, M. S. M.; Nazar, R.: Comparison between the homotopy analysis method and homotopy perturbation method to solve coupled Schrödinger–KdV equation, Journal of applied mathematics and computing, No. 31, 1-12 (2009) · Zbl 1177.65152 · doi:10.1007/s12190-008-0187-4
[17]Alomari, A. K.; Noorani, M. S. M.; Nazar, R.: The homotopy analysis method for the exact solutions of the K(2,2), Burgers and coupled Burgers equations, Applied mathematical sciences 2, No. 40, 1963-1977 (2008) · Zbl 1154.35438 · doi:http://www.m-hikari.com/ams/ams-password-2008/ams-password37-40-2008/alomariAMS37-40-2008.pdf
[18]Khan, H.; Mohapatra, R. N.; Vajravelu, K.; Liao, S. J.: The explicit series solution of SIR and SIS epidemic models, Applied mathematics and computation 215, 653-669 (2009) · Zbl 1171.92033 · doi:10.1016/j.amc.2009.05.051
[19]Liao, S. -J.: Beyond perturbation: introduction to the homotopy analysis method, (2003)
[20]Odibat, M.: A study on the convergence of homotopy analysis method, Applied mathematics and computation 217, 782-789 (2010) · Zbl 1203.65105 · doi:10.1016/j.amc.2010.06.017
[21]Liao, S. J.: Comparison between the homotopy analysis method and homotopy perturbation method, Applied mathematics and computation 169, 1186-1194 (2005) · Zbl 1082.65534 · doi:10.1016/j.amc.2004.10.058
[22]Liao, S. J.: An optiomal homotopy-analysis approach for strongly nonlinear differential equation, Communications in nonlinear science and numerical simulation 15, 2003-2016 (2010) · Zbl 1222.65088 · doi:10.1016/j.cnsns.2009.09.002
[23]Niu, Z.; Wang, C.: A one-step optimal homotopy analysis method for nonlinear differential equations, Communication in nonlinear science and numerical simulation 15, 2026-2036 (2010) · Zbl 1222.65091 · doi:10.1016/j.cnsns.2009.08.014