numerical solution of a system of volterra integral equations in application to the avian human influenza epidemic model

We propose an efficient multistage method for solving a system of linear and nonlinear volterra integral equations of the second kind. this numerical method is based on the gauss–legendre quadrature rule that obtains several values of unknown function at each step, and it will be shown that the order of the convergence is o(𝑀^−4), where 𝑀 is the number of the nodes in the time discretization. the method has also the advantages of simplicity of application, less computational time, and useful performance for large intervals. in order to show the efficiency of the method, numerical results for the avian human influenza epidemic model is obtained that is comparable with the fourth-order runge–kutta method.