scholarly journals Construction of the solution of the boundary value problem for integro differential equation with a small parameter in highest derivatives

2016 ◽  
Vol 84 (4) ◽  
pp. 99-103
Author(s):  
A.E. Mirzakulova ◽  
◽  
N. Atakhan ◽  
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Small Parameter ◽  
Boundary Value ◽  
Integro Differential Equation

scholarly journals On a nonlinear boundary value problem involving a small parameter

1962 ◽  
Vol 2 (4) ◽  
pp. 425-439 ◽  
Author(s):  
A. Erdéyi
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Small Parameter ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Ordinary Differential Equation ◽  
Nonlinear Boundary Value Problem ◽  
Image Position

In this paper we shall discuss the boundary value problem consisting of the nonlinear ordinary differential equation of the second order, and the boundary conditions.

ON AN INTEGRO-DIFFERENTIAL EQUATION OF PSEUDOPARABOLIC-PSEUDOHYPERBOLIC TYPE WITH DEGENERATE KERNELS

2018 ◽  
Vol 52 (1 (245)) ◽  
pp. 19-26 ◽  
Author(s):  
T.K. Yuldashev
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Fourier Method ◽  
Integro Differential Equation ◽  
The One

In the article the questions of solvability of boundary value problem for a homogeneous pseudoparabolic-pseudohyperbolic type integro-differential equation with degenerate kernels are considered. The Fourier method based on separation of variables is used. A criterion for the one-valued solvability of the considering problem is found. Under this criterion the one-valued solvability of the problem is proved.

scholarly journals A PROBLEM WITH PARAMETER FOR THE INTEGRO-DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 26 (1) ◽  
pp. 34-54
Author(s):  
Elmira A. Bakirova ◽  
Anar T. Assanova ◽  
Zhazira M. Kadirbayeva
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Cauchy Problems ◽  
Algebraic Equations ◽  
Integro Differential Equation ◽  
Loaded Differential Equation ◽  
Linear Algebraic Equations

The article proposes a numerically approximate method for solving a boundary value problem for an integro-differential equation with a parameter and considers its convergence, stability, and accuracy. The integro-differential equation with a parameter is approximated by a loaded differential equation with a parameter. A new general solution to the loaded differential equation with a parameter is introduced and its properties are described. The solvability of the boundary value problem for the loaded differential equation with a parameter is reduced to the solvability of a system of linear algebraic equations with respect to arbitrary vectors of the introduced general solution. The coefficients and the right-hand sides of the system are compiled through solutions of the Cauchy problems for ordinary differential equations. Algorithms are proposed for solving the boundary value problem for the loaded differential equation with a parameter. The relationship between the qualitative properties of the initial and approximate problems is established, and estimates of the differences between their solutions are given.

Sign in / Sign up

Export Citation Format

Share Document