Legendre spectral collocation method for solving fractional SIRC model and influenza A
In this paper, Legendre spectral method is presented to study the approximate solution of fractional SIRC model. The fractional derivative is described in the Caputo sense. The properties of the Legendre polynomials are used to reduce the proposed method to the solution of nonlinear system of algebraic equations using Newton iteration method. Moreover, the convergence analysis and an upper bound of the error for the derived formula are given. We compared our numerical solutions with those numerical solutions using fourth-order Rung-Kutta method. The obtained results of the SIRC model show the simplicity and the efficiency of the proposed method.
fractional sirc model legendre spectral method convergence analysis fourth-order rung-kutta method caputo fractional derivative