جواب تقریبی مدلی از عفونت HIVCD4+T از مرتبه کسری غیر خطی با استفاده از روش تابع پایه شعاعی ربع دیفرانسیلی
Subject Areas : Numerical Analysisکوکب چلمبری 1 , حمیده ابراهیمی 2 , زینب آیاتی 3
1 - گروه ریاضی، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران
2 - گروه ریاضی کاربردی، دانشکده علوم پایه، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران
3 - گروه علوم مهندسی، دانشکده فنی و مهندسی شرق گیلان، دانشگاه گیلان، رودسر-واجارگاه، ایران
Keywords: finite difference method, Caputo fractional derivative, Radial Basis Function Method (RBFM), Differential Quadrature Radial Basis Function Method, (DQ-RBFM), CD4+Tcells,
Abstract :
In this research, differential quadrature radial basis functions Method is performed to a fractional order model of HIV infection of CD4+T. Here, Caputo fractional derivative is used and it is approximated by forward finite difference method. Results have been compared with the results of Laplace Adomian decomposition method (LADM), Laplace Adomian decomposition method-pade (LADM-pade), Runge-Kutta, Variational iteration method (VIM) and Variational iteration method-pade (VIM-Pade) for α_1=α_2=α_3 and residual functions have been plotted. And also approximate solutions of suggested method for different order of fractional derivatives have been shown.
Ahmadi, N., Vahidi, A. R., & Allahviranloo, T. (2017). An efficient approach based on radial basis functions for solving stochastic fractional differential equations. Math. Sci, 11, 113–118.
Arafa, A. A. M., Hanafy. I. M., & Gouda. M. I. (2016). Stability analysis of fractional order-HIV Infection of CD4+T cells with numerical solutions, Journal of Fractional Calculus and Applications, 7 (1) 36-45.
Biazar, J., Sadri, Kh., & Ebrahimi, H. (2011). Variational iteration method for a model of HIV infection of cells. Journal of Nature Science and Sustainable Technology, 2, 83-90.
Biazar, J., Hosseini, K. (2016). A modified Adomian decomposition method for singular initial value Emden-Fowler type equations. International Journal of Applied Mathematical Research, 5, 69-72.
Biazar, J., Ebrahimi, H. (2009). Variational Iteration Method for Fredholm integral equations of the second kind. Iranian Journal of Optimization, 1,11-17.
Biazar, J., Hosseini, K. (2017). An Effective modification of Adomian Decomposition Method for Solving Emden-Fowler Type Systems. The National Academy of Sciences, 40, 258-209.
Biazar, J., Hosseini, K. (2017). Analytic approximation of Volterra’s population model, Journal of Applied Mathematics Statistics and Informatics, 13, 5-17.
Chandhini, G., Prashanthi, K. S., & Antony, V. (2017), A radial basis function method for fractional Darboux problems. Engineering Analysis with Boundary Elements, 000, 1-18.
Dehghan, M., &Abbaszadeh, M. (2017). Solution of multi-dimensional Klein–Gordon–Zakharov and Schrödinger /Gross–Pitaevskii equations via local Radial Basis Functions–Differential Quadrature (RBF–DQ) technique on non-rectangular computational domain. Engineering Analysis with Boundary Elements,000, 1-15.
Dehghan, M., & Abbaszadeh, M. (2018). A combination of proper orthogonal decomposition–discrete empirical interpolation method (POD–DEIM) and meshless local RBF-DQ approach for prevention of groundwater contamination. Computers and Mathematics with Applications, 75, 1390-1412.
Dehghan,M., & Abbaszadeh,M. (2018) . An upwind local radial basis functions-differential quadrature (RBF-DQ) method with proper orthogonal decomposition (POD) approach for solving compressible Euler equation, Engineering Analysis with Boundary Elements, 000, 1-13.
Gökdogan, A., Yildirim, A., & Merdan, M. (2011). Solving a fractional order model of HIV infection of CD4+ T cell, Mathematical and Computer Modelling, 54, 2132–2138.
Hardy, R, L. (1971). Multiquadric equations of topography and other irregular surface, Journal of geophysical research, 76, 1905-1915.
Hosseini, K., Biazar, J., Ansari, R., & Gholamin, P. (2012). A new algorithm for solving differential equations. Math. Meth. Appl. Sci, 35, 993–999.
Hosseini, K., Daneshian, B., Amanifard, N., & Ansari, R. (2012). Homotopy Analysis Method for a Fin with Temperature Dependent Internal Heat Generation and Thermal Conductivity. International Journal of Nonlinear Science, 14, 201-210.
Ilie, M., Biazar, J., Ayati, Z. (2017). Application of the Lie Symmetry Analysis for Second-order Fractional Differential Equations. Iranian Journal of Optimization, 2, 79-83.
Kansa, E. (1990). Multiquadrics a scattered data approximation scheme with Applications and to computational fluid dynamics–I surface approximations and partial derivative estimates. Computers & Mathematics with Applications, 19, 147–161.
Karamali., G., Dehghan, M., & Abbaszadeh, M. (2018). Numerical solution of a time fractional PDE in the electroanalytical chemistry by a local meshless method. Engineering with Computers published online.
Kazem, S., & Hatam, A. (2017). A modification on strictly positive definite RBF-DQ method based on matrix decomposition. Engineering Analysis with Boundary Elements, 76, 90-98.
Liu, J., Li, X., & Hu, X. (2019). A RBF-based differential quadrature method for solving two-dimensional variable-order time fractional advection-diffusion equation. Journal of Computational Physics. 384, 222-238.
Moradweysi, P., Ansari, R., Hosseini, K., & Sadeghi, F. (2018). Application of modified Adomian decomposition method to pull-in instability of nano-switches using nonlocal Timoshenko beam theory. Applied Mathematical Modelling, 54, 594-604.
Ongun,M. Y. (2011). The Laplace Adomian Decomposition Method for solving a model for HIV infection of CD4+T cells. Mathematical and Computer Modelling, 53, 597–603.
Parand, K., & Hashemi, S. (2018). RBF-DQ Method for Solving Equations of Lane-Emden type. Ain Shams Engineering Journal, 4, 615-629.
Senthilkumaran, M., & Arul Joseph, G. (2017). Stability Analysis for Fractional Order Model of HIV infection of CD4+T-Cells with Independent Delays. International Journal of Computational and Applied Mathematics, 12, 635-645.
