scholarly journals A Note On The Stability of Solution for Elliptic-Schrödinger Type Nonlocal Boundary Value Problem

2020 ◽  
Author(s):  
Yildirim OZDEMİR
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Stability Of Solution ◽  
The Stability

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 well-posedness of the nonlocal boundary value problem for parabolic difference equations

2004 ◽  
Vol 2004 (2) ◽  
pp. 273-286 ◽  
Author(s):  
A. Ashyralyev ◽  
I. Karatay ◽  
P. E. Sobolevskii
Keyword(s):  
Boundary Value Problem ◽  
Difference Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Well Posedness ◽  
Nonlocal Boundary Value Problem ◽  
The Difference ◽  
Type Boundary ◽  
The Stability

We consider the nonlocal boundary value problem for difference equations(uk−uk−1)/τ+Auk=φk,1≤k≤N,Nτ=1, andu0=u[λ/τ]+φ,0<λ≤1, in an arbitrary Banach spaceEwith the strongly positive operatorA. The well-posedness of this nonlocal boundary value problem for difference equations in various Banach spaces is studied. In applications, the stability and coercive stability estimates in Hölder norms for the solutions of the difference scheme of the mixed-type boundary value problems for the parabolic equations are obtained. Some results of numerical experiments are given.

scholarly journals FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Fatma Songul Ozesenli Tetikoglu
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Elliptic Partial Differential Equation ◽  
Dirichlet Condition ◽  
Stability Estimates ◽  
Nonlocal Boundary Value Problem ◽  
Numerical Examples ◽  
The Stability

A numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze-Samarskii-Dirichlet condition. The first and second-orders of accuracy stable difference schemes for the approximate solution of this nonlocal boundary value problem are presented. The stability estimates, coercivity, and almost coercivity inequalities for solution of these schemes are established. The theoretical statements for the solutions of these nonlocal elliptic problems are supported by results of numerical examples.

scholarly journals On second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 56 (1) ◽  
pp. 143-153 ◽  
Author(s):  
Katarzyna Szymańska-Dębowska
Keyword(s):  
Boundary Value Problem ◽  
Bounded Variation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

Abstract This work is devoted to the existence of solutions for a system of nonlocal resonant boundary value problem $$\matrix{{x'' = f(t,x),} \hfill & {x'(0) = 0,} \hfill & {x'(1) = {\int_0^1 {x(s)dg(s)},} }} $$ where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation.

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