Triangular functions for numerical solution of the nonlinear Volterra integral equations

被引：15

作者：

Kazemi, Manochehr ^{[1
]}

机构：

[1] Islamic Azad Univ, Dept Math, Ashtian Branch, Ashtian, Iran

来源：

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2022年 / 68卷 / 03期

关键词：

Iterative method; Triangular functions; Uniform modulus of continuity; Successive approximations; 2ND KIND; SUCCESSIVE INTERPOLATIONS; QUADRATURE-RULES; FREDHOLM; EXISTENCE; WAVELETS; TAYLOR;

D O I：

10.1007/s12190-021-01603-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a new numerical iterative method based on the successive approximations method for solving nonlinear Hammerstein Volterra integral equations of the second kind is proposed. The main approximation tool is based on triangular functions. Also, the convergence analysis and numerical stability of the proposed method are proved. Finally, some numerical examples verify the theoretical results and show the accuracy of the method.

引用

页码：1979 / 2002

页数：24

共 50 条

[21] A new strategy for the numerical solution of nonlinear Volterra integral equations with vanishing delays
Zhang Xiao-yong
APPLIED MATHEMATICS AND COMPUTATION, 2020, 365
[22] An iterative technique for the numerical solution of nonlinear stochastic Ito -Volterra integral equations
Saffarzadeh, M.
Loghmani, G. B.
Heydari, M.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 333 : 74 - 86
[23] On the numerical solution of linear and nonlinear volterra integral and integro-differential equations
Mohsen, Adel
El-Gamel, Mohamed
APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (07) : 3330 - 3337
[24] Numerical solution of nonlinear stochastic Itô–Volterra integral equations based on Haar wavelets
Jieheng Wu
Guo Jiang
Xiaoyan Sang
Advances in Difference Equations, 2019
[25] Numerical implementation of triangular functions for solving a stochastic nonlinear volterra-fredholm integral equation
Sadati, Z.
IAENG International Journal of Applied Mathematics, 2015, 45 (02) : 102 - 107
[26] Error estimation and numerical solution of nonlinear fuzzy Fredholm integral equations of the second kind using triangular functions
Baghmisheh, Mahdi
Ezzati, Reza
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2016, 30 (02) : 639 - 649
[27] The approximating functions method for nonlinear Volterra integral equations
A. Nerukh
D. Zolotariov
T. Benson
Optical and Quantum Electronics, 2015, 47 : 2565 - 2575
[28] The approximating functions method for nonlinear Volterra integral equations
Nerukh, A.
Zolotariov, D.
Benson, T.
OPTICAL AND QUANTUM ELECTRONICS, 2015, 47 (08) : 2565 - 2575
[29] Numerical Solutions of a Class of Nonlinear Volterra Integral Equations
Malindzisa, H. S.
Khumalo, M.
ABSTRACT AND APPLIED ANALYSIS, 2014,
[30] On the Stability of Numerical Methods for Nonlinear Volterra Integral Equations
Messina, E.
Muroya, Y.
Russo, E.
Vecchio, A.
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2010, 2010

← 1 2 3 4 5 →