scholarly journals Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Okan Gercek
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
Well Posedness ◽  
Hölder Spaces ◽  
Order Of Accuracy ◽  
First Order ◽  
Accuracy Difference ◽  
Holder Spaces

scholarly journals On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic-Parabolic Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Okan Gercek
Keyword(s):  
Approximate Solution ◽  
Difference Scheme ◽  
Parabolic Equations ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Parabolic Problems ◽  
Well Posedness ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
Accuracy Difference

A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem−d2u(t)/dt2+Au(t)=g(t),(0≤t≤1),du(t)/dt−Au(t)=f(t),(−1≤t≤0),u(1)=u(−1)+μfor differential equations in a Hilbert spaceHwith a self-adjoint positive definite operatorAis considered. The well posedness of this difference scheme in Hölder spaces is established. In applications, coercivity inequalities for the solution of a difference scheme for elliptic-parabolic equations are obtained and a numerical example is presented.

scholarly journals On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Allaberen Ashyralyev ◽  
Okan Gercek
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Approximate Solutions ◽  
Second Order ◽  
Well Posedness ◽  
Parabolic Differential Equations ◽  
Implicit Difference Scheme ◽  
Order Of Accuracy

We are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness of this difference scheme is established. In an application, coercivity estimates in Hölder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic-parabolic differential equations are obtained.

scholarly journals On the NBVP for semilinear hyperbolic equations

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 999-1007
Author(s):  
Necmettin Aggez ◽  
Gulay Yucel
Keyword(s):  
Hilbert Space ◽  
Difference Scheme ◽  
Hyperbolic Equations ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Order Of Accuracy ◽  
Convergence Estimate ◽  
First Order ◽  
Accuracy Difference ◽  
Semilinear Hyperbolic Equation

This paper is concerned with establishing the solvability of the nonlocal boundary value problem for the semilinear hyperbolic equation in a Hilbert space. For the approximate solution of this problem, the first order of accuracy difference scheme is presented. Under some assumptions, the convergence estimate for the solution of this difference scheme is obtained. Moreover, these results are supported by a numerical example.

Source identification problems for hyperbolic differential and difference equations

2019 ◽  
Vol 27 (3) ◽  
pp. 301-315 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Fathi Emharab
Keyword(s):  
Difference Scheme ◽  
Source Identification ◽  
Identification Problem ◽  
Stability Estimates ◽  
Identification Problems ◽  
Order Of Accuracy ◽  
One Dimensional ◽  
First Order ◽  
Accuracy Difference ◽  
The Difference

Abstract In the present study, a source identification problem for a one-dimensional hyperbolic equation is investigated. Stability estimates for the solution of the source identification problem are established. Furthermore, a first-order-of-accuracy difference scheme for the numerical solution of the source identification problem is presented. Stability estimates for the solution of the difference scheme are established. This difference scheme is tested on an example, and some numerical results are presented.

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