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 $(t-τ)^{α-1}$ with $0 <α<1.$ 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.