An epidemiology model involving high-order linear Fredholm integro-differential-difference equations via a novel balancing collocation technique

Abstract

In this study, the approximations of the higher order linear Fredholm integro-differential-difference equations (IDDEs), with the mixed conditions, have been performed by a new collocation technique based on the balancing polynomials. In particular, an attempt has been made to transform the linear IDDEs and the given boundary conditions into matrix equations which corresponds to a system of linear algebraic equations via the proposed procedure. In addition to that, the solutions obtained by the proposed numerical methodology have been analogized with the exact solutions and the error has been registered to manifest the accuracy of the solutions. Furthermore, the reliability and effectiveness of the proposed scheme have been illustrated by some numerical experiments. In addition to that, the error analysis of the technique has been performed along with the investigation of the error function for the improved approximate solutions for the IDDEs. In particular, the rate of approximation of the balancing polynomials has been deduced and the numerical accuracy of the suggested technique has been demonstrated. Apart from that, the absolute errors have been tabulated and graphical figures have been depicted for the solutions obtained via the proposed technique.