numerical solution of an influenza model with vaccination and antiviral treatment by the newton-chebyshev polynomial method

We consider a mathematical model of an influenza disease with vaccination and antiviral treatment. this model is expressed by a system of nonlinear ordinary differential equations. we linearize this system by the newton’s method and obtain a sequence of linear systems. the linear systems can be solved by the chebyshev polynomial solutions, which is a convergence method for numerical solution of linear systems. we solve the problem on a union of many partial intervals. in each partial interval, we first obtain a crude approximation for starting the newton’s method, then solve the problem on current interval by using the lag intervals. an illustration of procedures, we give an algorithm for the initial guess and apply this algorithm for obtaining the total algorithm of the method. we investigate the convergence conditions of the newton’s method for the presented model. in the numerical examples section, we provide some numerical examples to illustrate of the accuracy of the method, and see that the main criterion of the convergence is true for such problems.