Uniform convergence of the difference scheme for one nonstationary nonlocal boundary-value problem

1991 ◽  
Vol 2 (3) ◽  
pp. 223-228
Author(s):  
N. I. Ionkin
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Uniform Convergence ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
The 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.

A High-Order Difference Scheme for a Nonlocal Boundary-Value Problem for the Heat Equation

2001 ◽  
Vol 1 (4) ◽  
pp. 398-414 ◽  
Author(s):  
Zhi-Zhong Sun
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
High Order ◽  
Order Difference ◽  
Local Boundary ◽  
Non Local ◽  
The Difference ◽  
Boundary Equations

Abstract This paper is concerned with a high order difference scheme for a non- local boundary-value problem of parabolic equation. The integrals in the boundary equations are approximated by the composite Simpson rule. The unconditional solv- ability and L_∞ convergence of the difference scheme is proved by the energy method. The convergence rate of the difference scheme is second order in time and fourth order in space. Some numerical examples are provided to illustrate the convergence.

On the Fourth Order of Accuracy Difference Scheme for the Bitsadze-Samarskii Type Nonlocal Boundary Value Problem

2011 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Elif Ozturk ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Fourth Order ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Order Of Accuracy ◽  
Accuracy Difference

scholarly journals An Approximation of Semigroups Method for Stochastic Parabolic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Mehmet Emin San
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Single Step ◽  
Nonlocal Boundary Value Problem ◽  
Convergence Estimate ◽  
Numerical Examples ◽  
Convergence Estimates ◽  
The Difference

A single-step difference scheme for the numerical solution of the nonlocal-boundary value problem for stochastic parabolic equations is presented. The convergence estimate for the solution of the difference scheme is established. In application, the convergence estimates for the solution of the difference scheme are obtained for two nonlocal-boundary value problems. The theoretical statements for the solution of this difference scheme are supported 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.

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