Atlas: A note on the nonlocal boundary value problem for parabolic difference equations: well-posedness by Allaberen Ashyralyev

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ICDS International Conference on Dynamical Systems 2007
June 26-30, 2007
Abant Izzet Baysal University
Bolu, Turkey

Organizers
Cenap Özel (Bolu, Turkey), Mreza Molaei (Kerman, Iran), Figen Çilingir (Ankara, Turkey)

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A note on the nonlocal boundary value problem for parabolic difference equations: well-posedness
by
Allaberen Ashyralyev
Department of Mathematics, Fatih University, Istanbul, Turkey

Abstract

The high order of accuracy Pade difference schemes for approximate solution of the nonlocal boundary value problem

v^{^'}(t)+Av(t)=f(t)(0 ≤ t ≤ 1), v(0)=v(l)+m, 0 < l ≤ 1

for differential equation in an arbitrary Banach space E with the strongly positive operator A are considered. The well-posedness of these difference schemes is established. In applications, the almost coercive stability and the coercive stability estimates for the solutions of difference schemes for the approximate solutions of the nonlocal boundary value problems for parabolic equations are obtained.

Key Words: Parabolic equation; Nonlocal boundary value problem; Pade's difference schemes; High order of accuracy; Well-posedness; Coercive inequalities

AMS(MOS) subject classifications: 65 N, 47 D, 34 B

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Date received: March 24, 2007