About a New Nonlinear Integro-Differential Equation of Volterra-Strum-Liouville Type with a Weakly Singular Kernel

被引：0

作者：

Mezhoud, Djaafer ^{[1
]}

Benssaad, Meryem ^{[2
]}

Lemita, Samir ^{[3
]}

Khellaf, Ammar ^{[1
]}

机构：

[1] Natl Polytech Coll Constantine, Engn Coll, Preparatory Class Dept, El Khroub, Algeria

[2] Higher Normal Sch Technol Educ, Dept Math, Skikda, Algeria

[3] Normal Sch Ouargla, Ouargla, Algeria

来源：

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2024年 / 42卷

关键词：

Nonlinear Volterra integral equation; integro-differential equation; fixed point; product integration method;

D O I：

10.5269/bspm.63648

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This present paper proposes an analytical and a numerical study of a new integro-differential Volterra-Strum-Liouville equation of the second type, having a weak singularity. We provide conditions that guarantee the existence and uniqueness of the solution to the nonlinear problem. Then, we develop a numerical technique using the production integration method. The numerical application shows the efficiency of the proposed procedure.

引用

页数：13

共 13 条

[1] ANALYSIS OF A NONLINEAR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATION
Aissaoui, M. Z.
Bounaya, M. C.
Guebbai, H.
[J]. QUAESTIONES MATHEMATICAE, 2022, 45 (02) : 307 - 325
[2] Atkinson K., 2001, THEORETICAL NUMERICA
[3] Bounaya MC, 2021, INT J COMPUT SCI MAT, V13, P194
[4] HIGH-ORDER METHODS FOR A CLASS OF VOLTERRA INTEGRAL-EQUATIONS WITH WEAKLY SINGULAR KERNELS
DE HOOG, F
WEISS, R
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1974, 11 (06) : 1166 - 1180
[5] Analytical and numerical study for an integro-differential nonlinear volterra equation with weakly singular kernel
Ghiat, Mourad
Guebbai, Hamza
[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (04) : 4661 - 4674
[6] New theoretical conditions for solving functional nonlinear equations by linearization then discretization
Khellaf, Ammar
Aissaoui, Mohamed Zine
[J]. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2022, 13 (01): : 2857 - 2869
[7] New numerical process solving nonlinear infinite-dimensional equations
Khellaf, Ammar
Merchela, Wassim
Benarab, Sarra
[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2020, 39 (02)
[8] Ladopoulous E. G., 2000, Singular Integral Equations Linear and Non-Linear Theory and Its Applications in Science and Engineering
[9] Linz P., 1985, SIAM STUDIES APPL MA, V7, DOI DOI 10.1137/1.9781611970852
[10] Solution of an Integro-differential Nonlinear Equation of Volterra Arising of Earthquake Model
Salah, Selma
Guebbai, Hamza
Lemita, Samir
Aissaoui, Mohamed Zine
[J]. BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2022, 40

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