Multistep collocation methods for weakly singular Volterra integral equations with application to fractional differential equations

Abstract

We discuss the application of multistep collocation methods to Volterra integral equations which contain a weakly singular kernel $(t-\tau {)}^{\alpha -1}$ with $0<\alpha <1.$ Convergence orders of the methods are determined and their superconvergence is also analyzed. The paper closes with numerical examples and application to fractional differential equations.

arXiv commentThis paper has been withdrawn by the author due to finding some errors