Extrapolation for solving a system of weakly singular nonlinear Volterra integral equations of the second kind

被引：3

作者：

Han, Huilei ^{[2
]}

He, Xiaoming ^{[1
]}

Liu, Yaping ^{[2
]}

Lu, Tao ^{[2
]}

机构：

[1] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA

[2] Sichuan Univ, Coll Math, Chengdu 610064, Sichuan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2011年 / 88卷 / 16期

基金：

美国国家科学基金会;

关键词：

system of weakly singular nonlinear Volterra integral equations of the second kind; extrapolation; a posteriori error estimate; MECHANICAL QUADRATURE METHODS; 2ND-ORDER ELLIPTIC PROBLEMS; FINITE-ELEMENT METHODS; RICHARDSON EXTRAPOLATION; NUMERICAL-SOLUTION; SPLITTING EXTRAPOLATION; DIFFERENTIAL-EQUATIONS; APPROXIMATE SOLUTION; ERROR; EXPANSION;

D O I：

10.1080/00207160.2011.606903

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article discusses an extrapolation method for solving a system of weakly singular nonlinear Volterra integral equations of the second kind. Based on a generalization of the discrete Gronwall inequality and Navot's quadrature rule, the modified trapeziform quadrature algorithm is presented. The iterative algorithm for solving the discrete system possesses a high accuracy order O(h(2+alpha)). After the asymptotic expansion of errors is proved, we can obtain an approximation with a higher accuracy order using extrapolation. An a posteriori error estimation is provided. Some numerical results are presented to illustrate the efficiency of our methods.

引用

页码：3507 / 3520

页数：14

共 50 条

[1] Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind
Lu Tao
Huang Yong
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 324 (01) : 225 - 237
[2] A Fractional Spectral Collocation for Solving Second Kind Nonlinear Volterra Integral Equations with Weakly Singular Kernels
Haotao Cai
[J]. Journal of Scientific Computing, 2019, 80 : 1529 - 1548
[3] A Fractional Spectral Collocation for Solving Second Kind Nonlinear Volterra Integral Equations with Weakly Singular Kernels
Cai, Haotao
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2019, 80 (03) : 1529 - 1548
[4] Bernstein numerical method for solving nonlinear fractional and weakly singular Volterra integral equations of the second kind
Bica, Alexandru Mihai
Satmari, Zoltan
[J]. DOLOMITES RESEARCH NOTES ON APPROXIMATION, 2024, 17 : 33 - 43
[5] A Numerical Method for Weakly Singular Nonlinear Volterra Integral Equations of the Second Kind
Micula, Sanda
[J]. SYMMETRY-BASEL, 2020, 12 (11): : 1 - 15
[6] On solving 2D weakly singular Volterra integral equations of the second kind
Chakir, Y.
Safouhi, H.
[J]. NUMERICAL ALGORITHMS, 2024,
[7] Approximation methods for second kind weakly singular Volterra integral equations
Kant, Kapil
Nelakanti, Gnaneshwar
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 368
[8] New algorithm for the system of nonlinear weakly singular Volterra integral equations of the second kind and integro-differential equations
Han, Huilei
Liu, Yaping
Lu, Tao
He, Xiaoming
[J]. Journal of Information and Computational Science, 2010, 7 (06): : 1229 - 1236
[9] The Puiseux Expansion and Numerical Integration to Nonlinear Weakly Singular Volterra Integral Equations of the Second Kind
Wang, Tongke
Qin, Meng
Zhang, Zhiyue
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2020, 82 (03)
[10] The Puiseux Expansion and Numerical Integration to Nonlinear Weakly Singular Volterra Integral Equations of the Second Kind
Tongke Wang
Meng Qin
Zhiyue Zhang
[J]. Journal of Scientific Computing, 2020, 82

← 1 2 3 4 5 →