Superconvergence and linear stability of multistep collocation method applied to Volterra integral equations with delay function θ(t)

The main purpose of this paper is to propose the superconvergence and linear stability analysis of multistep collocation method which depend on r fixed number ofprevious time steps and m collocation points to solve the Volterra integral equationsof the second kind with nonlinear and non-vanishing delay. P. Darania and et al., constructed the multistep collocation method to solve a general class of nonlineardelay integral equations including two types of linear and nonlinear lag function θ(t)and investigated the convergence analysis of this method. This method have uniformorder m + r for any choice of collocation parameters. In this paper we shows that,the constructed method have a high uniform order of superconvergence (2m + 2r − 1)together with strong stability properties. Numerical examples are presented to confirmthis theoretical predictiont.