Improved Bessel collocation method for linear Volterra integro-differential equations with piecewise intervals and application of a Volterra population model

In this paper, an improved Bessel collocation method (IBCM) based on the residual correction technique is presented to solve the high-order linear Volterra integro-differential equation (VIDE) which involves a population model with piecewise intervals. Correction of the approximated solution is obtained using the residual function of the operator equation. The error differential equation, gained by residual function, is solved by the Bessel collocation method (BCM). By summing the approximate solution of the error differential equation with the approximate solution of VIDE with piecewise intervals, a better approximare solution is obtained. Also, an upper bound is given for the corrected approximate solutions. Numerical examples are given to demonstrate the efficiency of the method and the numerical results are compared by existing results. In addition, an application of the population model is given for the method.