Convergence analysis of multi-step collocation method to solve generalized auto-convolution Volterra integral equations
Parviz Darania, Saeed Pishbin, Azam Ebadi
Urmia University, Urmia, Iran
Keywords: auto-convolution Volterra integral equation, Convergence analysis, Multi-step collocation methods
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.
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