scholarly journals Stability of difference schemes for Bitsadze-Samarskii type nonlocal boundary value problem involving integral condition

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1027-1047 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Elif Ozturk
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Difference Schemes ◽  
Nonlocal Boundary Value Problem ◽  
Stability Of Difference Schemes ◽  
Gauss Elimination ◽  
Accuracy Difference ◽  
Gauss Elimination Method

In this study, the stable difference schemes for the numerical solution of Bitsadze-Samarskii type nonlocal boundary-value problem involving integral condition for the elliptic equations are studied. The second and fourth orders of the accuracy difference schemes are presented. A procedure of modified Gauss elimination method is used for solving these difference schemes for the two-dimensional elliptic differential equation. The method is illustrated by numerical examples.

scholarly journals The Numerical Solution of the Bitsadze-Samarskii Nonlocal Boundary Value Problems with the Dirichlet-Neumann Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Elif Ozturk
Keyword(s):  
Numerical Solution ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Difference Schemes ◽  
Neumann Condition ◽  
Nonlocal Boundary Value Problem ◽  
Numerical Examples ◽  
Gauss Elimination ◽  
Accuracy Difference ◽  
Gauss Elimination Method

We are interested in studying the stable difference schemes for the numerical solution of the nonlocal boundary value problem with the Dirichlet-Neumann condition for the multidimensional elliptic equation. The first and second orders of accuracy difference schemes are presented. A procedure of modified Gauss elimination method is used for solving these difference schemes for the two-dimensional elliptic differential equation. The method is illustrated by numerical examples.

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.

scholarly journals Nonlocal boundary value problem with Poissons operator on a rectangle and its difference interpretation

2020 ◽  
Vol 99 (3) ◽  
pp. 38-54
Author(s):  
D.M. Dovletov ◽  
◽  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Rectangular Domain ◽  
Nonlocal Boundary Value Problem ◽  
Weighted Integral ◽  
Accuracy Difference

In the present paper, differential and difference variants of nonlocal boundary value problem (NLBVP) for Poisson’s equation in open rectangular domain are studied. The existence, uniqueness and a priori estimate of classical solution are established. The second order of accuracy difference scheme is presented. The applications with weighted integral condition are provided in differential and difference variants.

scholarly journals Modified Crank-Nicolson Difference Schemes for Nonlocal Boundary Value Problem for the Schrödinger Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Ali Sirma
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Approximate Solutions ◽  
Difference Schemes ◽  
Nonlocal Boundary Value Problem ◽  
The Stability ◽  
Crank Nicolson

The nonlocal boundary value problem for Schrödinger equation in a Hilbert space is considered. The second-order of accuracy -modified Crank-Nicolson difference schemes for the approximate solutions of this nonlocal boundary value problem are presented. The stability of these difference schemes is established. A numerical method is proposed for solving a one-dimensional nonlocal boundary value problem for the Schrödinger equation with Dirichlet boundary condition. A procedure of modified Gauss elimination method is used for solving these difference schemes. The method is illustrated by numerical examples.

scholarly journals On a Nonlocal Boundary Value Problem of a State-Dependent Differential Equation

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2800
Author(s):  
Ahmed El-Sayed ◽  
Eman Hamdallah ◽  
Hanaa Ebead
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Stieltjes Integral ◽  
Nonlocal Boundary Value Problem ◽  
Absolutely Continuous ◽  
State Dependent ◽  
Infinite Point

In this paper, the existence of absolutely continuous solutions and some properties will be studied for a nonlocal boundary value problem of a state-dependent differential equation. The infinite-point boundary condition and the Riemann–Stieltjes integral condition will also be considered. Some examples will be provided to illustrate our results.

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