On a difference scheme of fourth order of accuracy for the Bitsadze-Samarskii type nonlocal boundary value problem

2012 ◽  
Vol 36 (8) ◽  
pp. 936-955 ◽  
Author(s):  
A. Ashyralyev ◽  
E. Ozturk
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Fourth Order ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Order Of Accuracy

scholarly journals On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
The Difference

This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

scholarly journals On a nonlocal boundary value problem for the equation fourth-order in partial derivatives

2021 ◽  
pp. 16-23
Author(s):  
О.Ш. Киличов
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Problem ◽  
Order Equation ◽  
Nonlocal Boundary Value Problem ◽  
Fourth Order Equation ◽  
Uniqueness Of A Solution

В данной статье изучается нелокальная задача для уравнения четвертого порядка в которой доказывается существование и единственность решения этой задачи. Решение построено явно в виде ряда Фурье, обоснованы абсолютная и равномерная сходимость полученного ряда и возможность почленного дифференцирования решения по всем переменным. Установлен критерий однозначной разрешимости поставленной краевой задачи. In this article, we study a nonlocal problem for a fourth-order equation in which the existence and uniqueness of a solution to this problem is proved. The solution is constructed explicitly in the form of a Fourier series; the absolute and uniform convergence of the obtained series and the possibility of term-by-term differentiation of the solution with respect to all variables are substantiated. A criterion for the unique solvability of the stated boundary value problem is established.

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