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

Document Type : Research Articles

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Department of Mathematics, Faculty of Science, Urmia University, P.O.Box 165, Urmia-Iran

Abstract

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 of
previous time steps and m collocation points to solve the Volterra integral equations
of 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 nonlinear
delay integral equations including two types of linear and nonlinear lag function θ(t)
and investigated the convergence analysis of this method. This method have uniform
order 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 confirm
this theoretical predictiont.

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