(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Non-standard Volterra integral equations (NVIEs) are in the category of non-linear Volterra integral equations (VIEs) which appear in certain mathematical modelling processes.In the current study, new multi-step collocation techniques have been employed to numerically address non-standard Volterra integral equations. Several established outcomes concerning convergence of the numerical solution for this problem are investigated. In conclusion, two test problems are thoroughly examined to substantiate theoretical accomplishments in practical terms. Also, we apply one-step and multi-step collocation methods to solve NVIEs and compare numerical results to show the efficiency and high accuracy of the proposed method.