scholarly journals General Linear Boundary Value Problem for the Second-Order Integro-Differential Loaded Equation with Boundary Conditions Containing Both Nonlocal and Global Terms

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
M. R. Fatemi ◽  
N. A. Aliyev
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Fredholm Property ◽  
Second Order ◽  
Linear Boundary ◽  
Loaded Equation ◽  
Linear Boundary Value Problem ◽  
General Boundary Value Problem

The paper is devoted to obtaining the sufficient conditions for Fredholm property for the general boundary value problem of the second-order linear integro-differential equation. Here, the boundary conditions corresponding with the boundary value problem contain both nonlocal and global terms.

On the Correctness of Linear Boundary Value Problems for Systems of Generalized Ordinary Differential Equations

1994 ◽  
Vol 1 (4) ◽  
pp. 343-351
Author(s):  
M. Ashordia
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Bounded Variation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Continuous Operator ◽  
Functions Of Bounded Variation ◽  
Linear Boundary ◽  
Generalized Ordinary Differential Equations ◽  
Linear Boundary Value Problem

Abstract The sufficient conditions are established for the correctness of the linear boundary value problem dx(t) = dA(t) · x(t) + df(t); l(x) = c 0, where and are matrix- and vector-functions of bounded variation, , and l is a linear continuous operator from the space of n-dimentional vector-functions of bounded variation into .

scholarly journals The Sign of the Green Function of an n-th Order Linear Boundary Value Problem

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 673
Author(s):  
Pedro Almenar Belenguer ◽  
Lucas Jódar
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Linear Boundary ◽  
Absolute Value ◽  
Partial Derivatives ◽  
The Green Function ◽  
Derivatives Of ◽  
Linear Boundary Value Problem

This paper provides results on the sign of the Green function (and its partial derivatives) of an n-th order boundary value problem subject to a wide set of homogeneous two-point boundary conditions. The dependence of the absolute value of the Green function and some of its partial derivatives with respect to the extremes where the boundary conditions are set is also assessed.

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhad H. Abregov ◽  
Vladimir Z. Kanchukoev ◽  
Maryana A. Shardanova
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Argument ◽  
Second Order Differential Equation

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

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