Convergence analysis of multi-step collocation method to solve generalized auto-convolution Volterra integral equations

In this study, we introduce multi-step collocation methods (MSCM) for solving the 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. A convergence analysis 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.