On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method

被引：2

作者：

Rahby, A. S. ^{[1
]}

Abdou, M. A. ^{[2
]}

Mosa, G. A. ^{[1
]}

机构：

[1] Benha Univ, Dept Math, Fac Sci, Banha 13518, Egypt

[2] Alexandria Univ, Fac Educ, Dept Math, Alexandria 21544, Egypt

来源：

INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS | 2022年 / 20卷

关键词：

nonlinear Fredholm-Volterra integral equations; Picard's method; homotopy analysis method and error analysis; NUMERICAL-SOLUTIONS; COLLOCATION METHOD;

D O I：

10.28924/2291-8639-20-2022-35

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we discuss the existence and uniqueness of the solution of the second kind nonlinear Volterra-Fredholm integral equations (NV-FIEs) which appear in mathematical modeling of many phenomena, using Picard's method. In addition, we use Banach fixed point theorem to show the solvability of the first kind NV-FIEs. Moreover, we utilize the homotopy analysis method (HAM) to approximate the solution and the convergence of the method is investigated. Finally, some examples are presented and the numerical results are discussed to show the validity of the theoretical results.

引用

页数：14

共 50 条

[1] Numerical solutions for nonlinear Volterra-Fredholm integral equations of the second kind with a phase lag
Mosa, Gamal A.
Abdou, Mohamed A.
Rahby, Ahmed S.
AIMS MATHEMATICS, 2021, 6 (08): : 8525 - 8543
[2] Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method
Ghasemi, M.
Kajani, M. Tavassoli
Babolian, E.
APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (01) : 446 - 449
[3] A New Analysis of Volterra-Fredholm Boundary Integral Equations of Second Kind
杨洪涛
Northeastern Mathematical Journal, 1997, (03) : 325 - 334
[4] Solving a System of Volterra-Fredholm Integral Equations of the Second kind via Fixed Point Method
Hasan, Talaat I.
Salleh, Shaharuddin
Sulaiman, Nejmaddin A.
INNOVATION AND ANALYTICS CONFERENCE AND EXHIBITION (IACE 2015), 2015, 1691
[5] A global method for solving second-kind Volterra-Fredholm integral equations
Fermo, Luisa
Mezzanotte, Domenico
Occorsio, Donatella
BIT NUMERICAL MATHEMATICS, 2025, 65 (02)
[6] On the Numerical Solutions for Nonlinear Volterra-Fredholm Integral Equations
Darania, Parviz
Pishbin, Saeed
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2022, 40
[7] Homotopy perturbation method for the mixed Volterra-Fredholm integral equations
Yildirim, Ahmet
CHAOS SOLITONS & FRACTALS, 2009, 42 (05) : 2760 - 2764
[8] Homotopy Analysis Method to Solve Two-Dimensional Nonlinear Volterra-Fredholm Fuzzy Integral Equations
Georgieva, Atanaska
Hristova, Snezhana
FRACTAL AND FRACTIONAL, 2020, 4 (01) : 1 - 14
[9] Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations
Yalçinbas, S
APPLIED MATHEMATICS AND COMPUTATION, 2002, 127 (2-3) : 195 - 206
[10] Existence of solutions of nonlinear fuzzy Volterra-Fredholm integral equations
Balachandran, K
Prakash, P
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2002, 33 (03): : 329 - 343

← 1 2 3 4 5 →