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

2012 ◽  
Author(s):  
Fatma Songul Ozesenli Tetikoglu
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Fourth Order ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Order Of Accuracy ◽  
Accuracy Difference

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 New solvability condition of 2-d nonlocal boundary value problem for Poisson’s operator on rectangle

2021 ◽  
Vol 2021 (1) ◽  
pp. 12-28
Author(s):  
Dovlet M. Dovletov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
A Priori Estimate ◽  
Rectangular Domain ◽  
Nonlocal Boundary Value Problem ◽  
Order Of Accuracy ◽  
Solvability Conditions ◽  
Accuracy Difference

Abstract Differential and difference interpretations of a nonlocal boundary value problem for Poisson’s equation in open rectangular domain are studied. New solvability conditions are obtained in respect of existence, uniqueness and a priori estimate of the classical solution. Second order of accuracy difference scheme is presented.

scholarly journals Well-Posedness of the Boundary Value Problem for Parabolic Equations in Difference Analogues of Spaces of Smooth Functions

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
A. Ashyralyev
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Approximate Solutions ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Well Posedness ◽  
Nonlocal Boundary Value Problem ◽  
Smooth Functions ◽  
Accuracy Difference

The first and second orders of accuracy difference schemes for the approximate solutions of the nonlocal boundary value problemv′(t)+Av(t)=f(t)(0≤t≤1),v(0)=v(λ)+μ,0<λ≤1, for differential equation in an arbitrary Banach spaceEwith the strongly positive operatorAare considered. The well-posedness of these difference schemes in difference analogues of spaces of smooth functions is established. In applications, the coercive stability estimates for the solutions of difference schemes for the approximate solutions of the nonlocal boundary value problem for parabolic equation are obtained.

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