Geodesic
Convergence analysis of multi-step collocation method to solve generalized auto-convolution Volterra integral equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 2, pp. 149-160
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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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     author = {P. Darania and S. Pishbin and A. Ebadi},
     title = {Convergence analysis of multi-step collocation method to solve generalized auto-convolution {Volterra} integral equations},
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P. Darania; S. Pishbin; A. Ebadi. Convergence analysis of multi-step collocation method to solve generalized auto-convolution Volterra integral equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 2, pp. 149-160. http://geodesic.mathdoc.fr/item/SJVM_2023_26_2_a2/

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