Convergence Analysis of Multi-Step Collocation Methods to Solve Generalized Auto-Convolution Volterra Integral Equations

被引：1
|
作者：
Darania, P. [1 ]
Pishbin, S. [1 ]
Ebadi, A. [1 ]
机构：
[1] Urmia Univ, Fac Sci, Dept Math, Orumiyeh, Iran
来源：
NUMERICAL ANALYSIS AND APPLICATIONS | 2023年 / 16卷 / 02期
关键词：
auto-convolution Volterra integral equation; convergence analysis; multi-step collocation methods; RATIONAL QUADRATURE METHOD;
D O I：
10.1134/S1995423923020039
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this study, we introduce multi-step collocation methods (MSCM) for solving a 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. The convergence 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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页码：123 / 134
页数：12
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