scholarly journals On The Stability of Nonlocal Boundary Value Problem for Schrödinger-Parabolic Equations

2020 ◽  
Author(s):  
Yildirim OZDEMİR
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
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 Coercive solvability of the nonlocal boundary value problem for parabolic differential equations

2001 ◽  
Vol 6 (1) ◽  
pp. 53-61 ◽  
Author(s):  
A. Ashyralyev ◽  
A. Hanalyev ◽  
P. E. Sobolevskii
Keyword(s):  
Banach Space ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Nonlocal Boundary Value Problem ◽  
Parabolic Differential Equations ◽  
Coercive Solvability ◽  
Coercive Stability

The nonlocal boundary value problem,v′(t)+Av(t)=f(t)(0≤t≤1),v(0)=v(λ)+μ(0<λ≤1), in an arbitrary Banach spaceEwith the strongly positive operatorA, is considered. The coercive stability estimates in Hölder norms for the solution of this problem are proved. The exact Schauder's estimates in Hölder norms of solutions of the boundary value problem on the range{0≤t≤1,xℝ n}for2m-order multidimensional parabolic equations are obtaine.

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.

Nonlocal boundary-value problem for parabolic equations

1994 ◽  
Vol 46 (12) ◽  
pp. 1795-1802 ◽  
Author(s):  
N. M. Zadorozhna ◽  
O. M. Mel'nik ◽  
B. I. Ptashnik
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem
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