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 
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/
@article{SJVM_2023_26_2_a2,
     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},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {149--160},
     year = {2023},
     volume = {26},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2023_26_2_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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