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

页码：25 / 54

页数：30

共 50 条

[31] On the convergence rate of collocation methods for Volterra integral equations with weakly singular oscillatory trigonometric kernels [J].

Wu, Qinghua ;

Sun, Mengjun .

RESULTS IN APPLIED MATHEMATICS, 2023, 17

[32] A Numerical Method for Weakly Singular Nonlinear Volterra Integral Equations of the Second Kind [J].

Micula, Sanda .

SYMMETRY-BASEL, 2020, 12 (11) :1-15

[33] A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels [J].

Zhang, Li ;

Huang, Jin ;

Pan, Yubin ;

Wen, Xiaoxia .

COMPLEXITY, 2019, 2019

[34] Singularity separation Chebyshev collocation method for weakly singular Volterra integral equations of the second kind [J].

Wang, Tongke ;

Lian, Huan ;

Ji, Lu .

NUMERICAL ALGORITHMS, 2024, 95 (04) :1829-1854

[35] A Product Integration Approach Based on New Orthogonal Polynomials for Nonlinear Weakly Singular Integral Equations [J].

M. Rasty ;

M. Hadizadeh .

Acta Applicandae Mathematicae, 2010, 109 :861-873

[36] Legendre spectral projection methods for linear second kind Volterra integral equations with weakly singular kernels [J].

Chakraborty, Samiran ;

Kant, Kapil ;

Nelakanti, Gnaneshwar .

INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2022, 13 (02) :1377-1397

[37] A Nyström method based on product integration for weakly singular Volterra integral equations with variable exponent [J].

Ma, Zheng ;

Stynes, Martin .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2025, 454

[38] The economized monic Chebyshev polynomials for solving weakly singular Fredholm integral equations of the first kind [J].

Shoukralla, E. S. ;

Markos, M. A. .

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2020, 13 (01)

[39] A New Computational Method for Solving Weakly Singular Fredholm Integral Hquations of the First Kind [J].

Shoukralla, E. S. ;

Kamel, M. ;

Markos, M. A. .

PROCEEDINGS OF 2018 13TH INTERNATIONAL CONFERENCE ON COMPUTER ENGINEERING AND SYSTEMS (ICCES), 2018, :202-207

[40] Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equations [J].

Galperin, EA ;

Kansa, EJ ;

Makroglou, A ;

Nelson, SA .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 115 (1-2) :193-211

← 1 2 3 4 5 →