A SOLUTION TO A NONLINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATION

被引：1

作者：

Assanova, Anar T. ^{[1
]}

Karakenova, Sayakhat G. ^{[1
,2
]}

Mynbayeva, Sandugash T. ^{[1
,3
]}

Uteshova, Rosa E. ^{[1
,4
]}

机构：

[1] Inst Math & Math Modeling MES RK, Alma Ata 050010, Kazakhstan

[2] Al Farabi Kazakh Natl Univ, Alma Ata 050040, Kazakhstan

[3] K Zhubanov Aktobe Reg Univ, Aktobe 030000, Kazakhstan

[4] Int Informat Technol Univ, Dept Math & Comp Modeling, Alma Ata 050034, Kazakhstan

来源：

QUAESTIONES MATHEMATICAE | 2024年 / 47卷 / 01期

关键词：

Nonlinear Fredholm integro-differential equations; special Cauchy problem; general solution; boundary value problem; BOUNDARY-VALUE-PROBLEMS; NUMERICAL-SOLUTION; SOLVE; ALGORITHM;

D O I：

10.2989/16073606.2023.2183157

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with a Fredholm integro-differential equation with non-linear integral term. By using the Dzhumabaev parametrization method, we reduce the equation to a special Cauchy problem and establish sufficient conditions for the existence of its unique solution. The solution to the special Cauchy problem is used to construct a new general solution to the Fredholm integro-differential equation. We investigate some properties of the new general solution and apply it to boundary value problems.

引用

页码：61 / 73

页数：13

共 50 条

[21] A numerical approach for solving nonlinear Fredholm integro-differential equation with boundary layer
Cakir, Musa
Ekinci, Yilmaz
Cimen, Erkan
[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (06):
[22] New General Solution to a Quasilinear Fredholm Integro-Differential Equation and Its Application
Assanova, A. T.
Mynbayeva, S. T.
[J]. LOBACHEVSKII JOURNAL OF MATHEMATICS, 2023, 44 (10) : 4231 - 4239
[23] Fredholm integral equation method for the integro-differential Schrodinger equation
Chang, Ick-Soon
Kang, Sheon-Young
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (10) : 2676 - 2685
[24] Numerical Solution for Linear Fredholm Integro-Differential Equation Using Touchard Polynomials
Abdullah, Jalil Talab
[J]. BAGHDAD SCIENCE JOURNAL, 2021, 18 (02) : 330 - 337
[25] Projection methods for approximate solution of a class of nonlinear Fredholm integro-differential equations
Mandal, Moumita
Kayal, Arnab
Nelakanti, Gnaneshwar
[J]. APPLIED NUMERICAL MATHEMATICS, 2023, 184 : 49 - 76
[26] A sequential approach for solving the Fredholm integro-differential equation
Berenguer, M. I.
Fernandez Munoz, M. V.
Garralda-Guillem, A. I.
Ruiz Galan, M.
[J]. APPLIED NUMERICAL MATHEMATICS, 2012, 62 (04) : 297 - 304
[27] Projection methods for approximate solution of a class of nonlinear Fredholm integro-differential equations
Mandal, Moumita
Kayal, Arnab
Nelakanti, Gnaneshwar
[J]. APPLIED NUMERICAL MATHEMATICS, 2023, 184 : 49 - 76
[28] Asymptotic behavior of the solution of a nonlinear integro-differential diffusion equation
T. A. Dzhangveladze
Z. V. Kiguradze
[J]. Differential Equations, 2008, 44 : 538 - 550
[29] Asymptotic behavior of the solution of a nonlinear integro-differential diffusion equation
Dzhangveladze, T. A.
Kiguradze, Z. V.
[J]. DIFFERENTIAL EQUATIONS, 2008, 44 (04) : 538 - 550
[30] Solution to a Singular Integro-Differential Equation
Pandey, J. N.
Seifeddine, Fayez
[J]. JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2010, 12 (01) : 321 - 336

← 1 2 3 4 5 →