A note on the second order of accuracy difference schemes for hyperbolic–parabolic equations

2005 ◽  
Vol 165 (3) ◽  
pp. 517-537 ◽  
Author(s):  
A. Ashyralyev ◽  
H.A. Yurtsever
Keyword(s):  
Parabolic Equations ◽  
Second Order ◽  
Difference Schemes ◽  
Order Of Accuracy ◽  
Accuracy Difference

Second Order of Accuracy Difference Schemes for Ultra Parabolic Equations

2011 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Serhat Yilmaz ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Parabolic Equations ◽  
Second Order ◽  
Difference Schemes ◽  
Order Of Accuracy ◽  
Accuracy Difference

Numerical solution of a source identification problem: Almost coercivity

2019 ◽  
Vol 27 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Abdullah Said Erdogan ◽  
Ali Ugur Sazaklioglu
Keyword(s):  
Numerical Solution ◽  
Source Identification ◽  
Identification Problem ◽  
Second Order ◽  
Numerical Results ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Accuracy Difference ◽  
Coercive Stability

Abstract The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

scholarly journals An Approximation of Ultra-Parabolic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Serhat Yılmaz
Keyword(s):  
Approximate Solution ◽  
Parabolic Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Difference Schemes ◽  
Order Of Accuracy ◽  
Numerical Examples ◽  
Accuracy Difference ◽  
Initial Boundary Value ◽  
Theoretical Results

The first and second order of accuracy difference schemes for the approximate solution of the initial boundary value problem for ultra-parabolic equations are presented. Stability of these difference schemes is established. Theoretical results are supported by the result of numerical examples.

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 Solution of NBVP for Multidimensional Hyperbolic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Necmettin Aggez
Keyword(s):  
Approximate Solution ◽  
Hyperbolic Equations ◽  
Second Order ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Hyperbolic Problems ◽  
Order Of Accuracy ◽  
Numerical Examples ◽  
Accuracy Difference ◽  
Multidimensional Hyperbolic Equations

We are interested in studying multidimensional hyperbolic equations with nonlocal integral and Neumann or nonclassical conditions. For the approximate solution of this problem first and second order of accuracy difference schemes are presented. Stability estimates for the solution of these difference schemes are established. Some numerical examples illustrating applicability of these methods to hyperbolic problems are given.

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