×

Quasilinearization-Lagrangian method to solve the HIV infection model of CD4\(^+\)T cells. (English) Zbl 1395.92095

Summary: In this paper, the quasilinearization and Lagrangian methods are used for solving a model of the HIV infection of CD4\(^+\)T cells. This approach is based on the Lagrangian method by using the collocation points of transformed Hermite polynomials. The quasilinearization method is used for converting the non-linear problem to a sequence of linear equations and the Hermite Lagrangian method is applied for solving linear equations at each iteration. In the end, the obtained results have been compared with some other well-known results and show that the present method is efficient.

MSC:

92C60 Medical epidemiology
41A10 Approximation by polynomials
41A05 Interpolation in approximation theory
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Funaro, D.: Polynomial Approximation of Differential Equations, 1st edn. Springer, Berlin (1992) · Zbl 0774.41010
[2] Gandomani, M Rasouli; Kajani, M Tavassoli, Numerical solution of a fractional order model of HIV infection of CD4\(^+\)T cells using munts-Legendre polynomials, Int. J. Bioautom., 20, 193-204, (2016)
[3] Gheorghiu, C.I.: Spectral Methods for Differential Problems. Institute of Numerical Analysis, Cluj-Napoca (2007) · Zbl 1122.65118
[4] Khalid, M; Sultana, M; Zaidi, F; Khan, F Sami, A numerical solution of a model for HIV infection CD4\(^+\)T cell, Int. J. Innovat. Sci. Res., 16, 79-85, (2015)
[5] Liverts, EZ; Krivec, R; Mandelzweig, VB, Quasilinearization approach to the resonance calculations: the quartic oscillator, Phys. Scripta, 77, 045004, (2008) · Zbl 1139.81339 · doi:10.1088/0031-8949/77/4/045004
[6] Merdan, M, Homotopy perturbation method for solving a model for HIV infection of CD4\(^+\)T-cells, Istab. Commerce Uni. J. Sci., 6, 39-52, (2007)
[7] Merdan, M; Gokdogan, A; Yildirim, A, On the numerical solution of the model for HIV infection of CD4\(^+\)T cells, Comput. Math. Appl., 62, 118-123, (2011) · Zbl 1228.65137 · doi:10.1016/j.camwa.2011.04.058
[8] Ongun, MY, The Laplace Adomian decomposition method for solving a model for HIV infection of CD4\(^+\)T cells, Math. Comput. Model., 53, 597-603, (2011) · Zbl 1217.65164 · doi:10.1016/j.mcm.2010.09.009
[9] Parand, K., Yousefi, H., Delkhosh, M., Ghaderi, A.: A novel numerical technique to obtain an accurate solution to the Thomas-Fermi equation, Euro. Phys. J. Plus, 131(7) 228, 1-16 (2016) · Zbl 1362.34039
[10] Parand, K; Delkhosh, M, An efficient numerical solution of nonlinear Hunter-Saxton equation, Commun. Theor. Phys., 67, 483-492, (2017) · Zbl 1365.35125 · doi:10.1088/0253-6102/67/5/483
[11] Parand, K; Delkhosh, M, Accurate solution of the Thomas-Fermi equation using the fractional order of rational Chebyshev functions, J. Comput. Appl. Math., 317, 624-642, (2017) · Zbl 1362.34039 · doi:10.1016/j.cam.2016.11.035
[12] Parand, K; Dehghan, M; Rezaei, AR; Ghaderi, SM, An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method, Comput. Phys. Comm., 181, 1096-1108, (2010) · Zbl 1216.65098 · doi:10.1016/j.cpc.2010.02.018
[13] Parand, K; Ghasemi, M; Rezazadeh, S; Peiravi, A; Ghorbanpour, A; Golpaygani, A Tavakoli, Quasilinearization approach for solving volterra’s population model, Appl. Comput. Math., 9, 95-103, (2010) · Zbl 1197.65229
[14] Parand, K; Rezaei, AR; Taghavi, A, Lagrangian method for solving Lane-Emden type equation arising in astrophysics on semi-infinite domains, Acta Astronaut., 67, 673-680, (2010) · doi:10.1016/j.actaastro.2010.05.015
[15] Parand, K; Ghaderi, A; Yousefi, H; Delkhosh, M, A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions, Electron. J. Differ. Equ., 2016, 1-18, (2016) · Zbl 1357.34035
[16] Perelson, AS; Kirschner, DE; Boer, R, Dynamics of HIV infection of CD4\(^+\)T cells, Math. Biosci., 114, 81-125, (1993) · Zbl 0796.92016 · doi:10.1016/0025-5564(93)90043-A
[17] Rezaei, A; Baharifard, F; Parand, K, Quasilinearization-barycentric approach for numerical investigation of the boundary value fin problem, Int. J. Comp. Elect. Auto. Cont. Info. Eng., 5, 194-201, (2011)
[18] Shen, J., Tang, T., Wang, L.-L.: Spectral Methods Algorithms, Analyses and Applications, 1st edn. Springer, Berlin (2010)
[19] Venkatesh, SG; Balachandar, S Raja; Ayyaswamy, SK; Balasubramanian, K, A new approach for solving a model for HIV infection of CD4\(^+\)T cells arising in mathematical chemistry using wavelates, J. Math. Chem., 54, 1072-1082, (2016) · Zbl 1364.92026 · doi:10.1007/s10910-016-0604-0
[20] Yuzbasi, S.: An exponential collocation method for the solutions of the HIV infection model of CD4\(^+\)T cells, Int. J. Biomath., 9(3) 1650036(15) (2016) · Zbl 1338.92066
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.