Analytical and Numerical Solutions of a Boundary Value Problem for Impulsive Differential Equations with Loadings

被引：3

作者：

Kadirbayeva, Zh. M. ^{[1
,2
]}

机构：

[1] Inst Math & Math Modeling, Dept Differential Equat, Alma Ata 050000, Kazakhstan

[2] Int Informat Technol Univ, Dept Math & Comp Modeling, Alma Ata 050040, Kazakhstan

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 12期

关键词：

impulsive differential equation; loadings; parametrization method; numerical algorithm; UNIQUE SOLVABILITY; INTEGRODIFFERENTIAL EQUATIONS; SYSTEMS; MODEL;

D O I：

10.1134/S199508022312017X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main interest of this paper is to propose a method in order to solve linear boundary value problem for impulsive differential equations with loadings. This method is called the Dzhumabaev parametrization method. The application of the this method leads the considering problem to a system of algebraic equations and Cauchy problems that are easy to solve. Some examples are introduced and the obtained results are compared with exact solution to illustrate the effectiveness and accuracy of the method.

引用

页码：5276 / 5285

页数：10

共 27 条

[1] Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations [J].

Abdullaev, V. M. ;

Aida-Zade, K. R. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2014, 54 (07) :1096-1109

[2] Successive approximation method for quasilinear impulsive differential equations with control [J].

Akhmetov, MU ;

Zafer, A .

APPLIED MATHEMATICS LETTERS, 2000, 13 (05) :99-105

[3] NUMERICAL IMPLEMENTATION OF SOLVING A BOUNDARY VALUE PROBLEM FOR A SYSTEM OF LOADED DIFFERENTIAL EQUATIONS WITH PARAMETER [J].

Assanova, A. T. ;

Bakirova, E. A. ;

Kadirbayeva, Zh. M. .

NEWS OF THE NATIONAL ACADEMY OF SCIENCES OF THE REPUBLIC OF KAZAKHSTAN-SERIES PHYSICO-MATHEMATICAL, 2019, 3 (325) :77-84

[4] On the numerical algorithms of parametrization method for solving a two-point boundary-value problem for impulsive systems of loaded differential equations [J].

Assanova, A. T. ;

Kadirbayeva, Zh. M. .

COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (04) :4966-4976

[5] Numerical Solution of Systems of Loaded Ordinary Differential Equations with Multipoint Conditions [J].

Assanova, A. T. ;

Imanchiyev, A. E. ;

Kadirbayeva, Zh. M. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2018, 58 (04) :508-516

[6]

Bainov D., 1993, Part of Pitman Monographs and Surveys in Pure and Applied Mathematics

[7]

Bakirova EA, 2017, B KARAGAND UNIV-MATH, V87, P43, DOI 10.31489/2017M3/43-50

[8] Stability analysis of a self-cycling fermentation model with state-dependent impulse times [J].

Cordova-Lepe, Fernando ;

Del Valle, Rodrigo ;

Robledo, Gonzalo .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2014, 37 (10) :1460-1475

[9] Loaded equations with periodic boundary conditions [J].

Dzhenaliev, MT .

DIFFERENTIAL EQUATIONS, 2001, 37 (01) :51-57

[10] On one approach to solve the linear boundary value problems for Fredholm integro-differential equations [J].

Dzhumabaev, D. S. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 294 :342-357

← 1 2 3 →