Convergence analysis of the product integration method for solving the fourth kind integral equations with weakly singular kernels

被引：13
作者：
Sajjadi, Sayed Arsalan [1 ]
Pishbin, Saeed [1 ]
机构：
[1] Urmia Univ, Dept Math, Fac Sci, Orumiyeh, Iran
来源：
NUMERICAL ALGORITHMS | 2021年 / 86卷 / 01期
关键词：
Numerical analysis; Weakly singular integral-algebraic equations; nu-Smoothing; Product integration; Convergence analysis; Tractability index; DIFFERENTIAL-ALGEBRAIC EQUATIONS; COLLOCATION METHODS; NUMERICAL-SOLUTION; SYSTEM;
D O I：
10.1007/s11075-020-00877-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider product integration method based on orthogonal polynomials to solve mixed system of Volterra integral equations of the first and second kind with weakly singular kernels. For investigation of the theoretical and numerical analysis of the mixed systems, the notions of the tractability index and nu-smoothing property are extended for a weakly singular Volterra integral operator. Convergence analysis of the product integration method is derived. Finally, the proposed method is illustrated by two examples, which confirm the theoretical prediction of the error estimation.
引用
收藏
页码：25 / 54
页数：30
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