Super implicit multistep collocation methods for nonlinear Volterra integral equations

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Abstract

In this paper, we construct a new class of multistep collocation methods for solving two types of nonlinear Volterra integral equations including nonstiff and stiff problems. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Convergence orders of the new methods are determined and a local superconvergence is described. Linear stability properties of the methods for both types are also analyzed and their efficiency is shown by numerical examples. © 2011 Elsevier Ltd.

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Fazeli, S., Hojjati, G., & Shahmorad, S. (2012). Super implicit multistep collocation methods for nonlinear Volterra integral equations. Mathematical and Computer Modelling, 55(3–4), 590–607. https://doi.org/10.1016/j.mcm.2011.08.034

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