Reliable iterative methods for mathematical biology model

Abstract

In this paper, three iterative methods will be used to solve the nonlinear differential equation systems that represents a model for HIV infection of cells. The iterative methods are the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM) to get the approximate solutions. Numerical solutions were also obtained by using the Runge-Kutta (RK4) method and good agreement have achieved. In addition, the convergence of proposed methods is present based on Banach's fixed point theorem. Also, comparisons are made between the proposed methods and the Adomian decomposition method (ADM), and the Variational iteration method (VIM), a good agreement have achieved without required to evaluate the Adomian polynomials to handle the nonlinear terms as in the ADM, does not require to calculate Lagrange multiplier as in the VIM and time saver. Moreover, the results of the maximum error remainder values are obtained and show that the proposed methods are effective and reliable. Our calculations were performed using the MATHEMATICA^®10.