## Related Articles

- Well-posedness of difference scheme for elliptic-parabolic equations in HÃ¶lder spaces without a weight. Ashyralyev, Allaberen; Gercek, Okan; Zusi, Emel // AIP Conference Proceedings;2014, Vol. 1611, p84
In the present paper, we are interested in studying a second order of accuracy difference scheme for the approximate solution of the elliptic-parabolic equation with the nonlocal boundary condition. Theorem on well-posedness of this problem in HÃ¶lder spaces without a weight is given. In an...

- On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations. Ashyralyev, Allaberen; Gercek, Okan // Abstract & Applied Analysis;2012, p1
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 HÃ¶lder norms for...

- On the well-posedness of a second order difference scheme for elliptic-parabolic equations in HÃ¶lder spaces. Gercek, Okan; Zusi, Emel // AIP Conference Proceedings;2015, Vol. 1676 Issue 1, p1
In this paper, we consider a second order of accuracy difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness results in HÃ¶lder spaces without a weight are presented. Coercivity estimates in HÃ¶lder norms for approximate...

- Nonlocal Boundary Value Problems for Elliptic-Parabolic Differential and Difference Equations. Ashyralyev, Allaberen; Gercek, Okan // Discrete Dynamics in Nature & Society;2008, p1
The article presents information on a study which investigated nonlocal boundary value problems for elliptic-parabolic differential and difference equations. The study assesses the well-posedness of this problem in HÃ¶lder spaces with a weight and the coercivity inequalities for the solution...

- Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in HÃ¶ lder Spaces. Gercek, Okan // Abstract & Applied Analysis;2012, p1
A first order of accuracy difference scheme for the approximate solution of abstract nonlocal boundary value problem -d2u(t)/dt2 + sign(t)Au(t) = g(t), (0 â‰¤ t â‰¤ 1), du(t)/dt + sign(t)Au(t) = f(t), (-1 â‰¤ t â‰¤ 0), u(0+) = u(0-), u'((0+) = u'((0-), and u(1) = u(-1) + Âµ for...

- Time-Nonlocal Boundary Value Problem for Degenerate Sobolev Type Equations. Pinigina, N. // Journal of Mathematical Sciences;Dec2015, Vol. 211 Issue 6, p811
We establish the solvability of time-nonlocal boundary value problems for degenerate Sobolev type equations with an elliptic-parabolic second order operator at the timederivative. We prove the uniqueness of a regular solution. Bibliography: 10 titles.

- NONLOCAL BOUNDARY-VALUE PROBLEMS FOR ELLIPTIC EQUATIONS: WELL-POSEDNESS IN BOCHNER SPACES. Ashyralyev, Allaberen // AIP Conference Proceedings;11/11/2010, Vol. 1309 Issue 1, p66
The well-posedness of the Bitsadze-Samarskii type nonlocal boundary value problem for abstract elliptic equations in Bochner spaces is established. The second order of accuracy difference scheme for the approximate solution of this problem is considered. The coercive inequalities for the...

- On the numerical solution of a two dimensional elliptic-parabolic equation. Gercek, Okan; Zusi, Emel // AIP Conference Proceedings;Sep2012, Vol. 1479 Issue 1, p606
In the present article, a numerical method for solving two dimensional elliptic-parabolic equations is studied. A procedure of modified Gauss elimination method is used for solving these difference schemes of two dimensional nonlocal boundary value problem for an elliptic-parabolic equation.

- Modified Crank-Nicolson Difference Schemes for Nonlocal Boundary Value Problem for the SchrÃ¶dinger Equation. Ashyralyev, Allaberen; Sirma, Ali // Discrete Dynamics in Nature & Society;2009, Special section p1
The nonlocal boundary value problem for SchrÃ¶dinger equation in a Hilbert space is considered. The second-order of accuracy r-modified Crank-Nicolson difference schemes for the approximate solutions of this nonlocal boundary value problem are presented. The stability of these difference...

- FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions. Ashyralyev, Allaberen; Ozesenli Tetikoglu, Fatma Songul // Abstract & Applied Analysis;2012, p1
A numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze-Samarskii-Dirichlet condition. The first and second-orders of accuracy stable difference schemes for the approximate solution of this...