Convergence Analysis of Multi-Step Collocation Methods to Solve Generalized Auto-Convolution Volterra Integral Equations

In this study, we introduce multi-step collocation methods (MSCM) for solving a Volterra Integral Equation (VIE) of the auto-convolution type such that without increasing the computational cost, the order of convergence of the proposed one-step collocation methods will be increased. The convergence of the MSCM is investigated using the Peano theorems for interpolation and, finally, two numerical examples are introduced to clarify the significant advantage of the MSCM.