This article is cited in 1 paper

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

P. Darania, S. Pishbin, A. Ebadi

Department of Mathematics, Faculty of Sciences, Urmia University, Urmia, Iran

Abstract: 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.

Key words: auto-convolution Volterra integral equation, convergence analysis, multi-step collocation methods.

MSC: 65R20, 65Q20, 45D05

Received: 20.05.2022
Revised: 21.11.2022
Accepted: 30.01.2023

DOI: 10.15372/SJNM20230203

 English version: Numerical Analysis and Applications, 2023, 16:2, 123–134