Okan Gercek

Nonlocal Boundary Value Problems for Elliptic-Parabolic Differential and Difference Equations

older spaces with a weight is established. The coercivity inequalities for the solution of boundary value problems for elliptic-parabolic equations are obtained. The first order of accuracy difference scheme for the approximate solution of this nonlocal boundary value problem is presented. The well-posedness of this difference scheme in H¨ older spaces is established. In applications, coercivity inequalities for the solution of a difference scheme for elliptic-parabolic equations are obtained. Copyright q 2008 A. Ashyralyev and O. Gercek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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

A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem , , , , for differential equations in a Hilbert space with a self-adjoint positive definite operator is considered. The well posedness of this difference scheme in Holder 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.

Finite difference method for multipoint nonlocal elliptic-parabolic problems

A finite difference method for solving the multipoint elliptic-parabolic partial differential equation with a nonlocal boundary condition is considered. Stable difference schemes accurate to first and second orders for this problem are presented. Stability, almost coercive stability and coercive stability for the solution of these difference schemes are obtained. The theoretical statements for the solution of these difference schemes are supported by numerical examples.

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

A first order of accuracy difference scheme for the approximate solution of abstract nonlocal boundary value problem −𝑑2𝑢(𝑡)/𝑑𝑡2

On the well-posedness of a second order difference scheme for elliptic-parabolic equations in Hölder spaces

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 Holder spaces without a weight are presented. Coercivity estimates in Holder norms for approximate solution of a nonlocal boundary value problem for elliptic-parabolic differential equation in an application are obtained.

On the numerical solution of a two dimensional elliptic-parabolic equation

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.

On a difference scheme of the second order of accuracy for elliptic-parabolic equations

The second order of accuracy difference scheme generated by Crank-Nicholson difference scheme for approximately solving multipoint nonlocal boundary value problem is considered. Well-posedness of this difference scheme in Hölder spaces is established. Furthermore, as applications, coercivity estimates in Hölder norms for approximate solutions of the multipoint nonlocal boundary value problems for mixed type equations are obtained. Moreover, the method is illustrated by numerical examples.

Numerical solution of a two dimensional elliptic-parabolic equation with Dirichlet-Neumann condition

In the present paper, a two dimensional elliptic-parabolic equation with Dirichlet-Neumann boundary condition is studied. The first and second order of accuracy difference schemes for the numerical solution of this problem are presented. Illustrative numerical results of these difference schemes are provided by using a procedure of modified Gauss elimination method.In the present paper, a two dimensional elliptic-parabolic equation with Dirichlet-Neumann boundary condition is studied. The first and second order of accuracy difference schemes for the numerical solution of this problem are presented. Illustrative numerical results of these difference schemes are provided by using a procedure of modified Gauss elimination method.

Well-posedness of difference scheme for elliptic-parabolic equations in Hölder spaces without a weight

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 Holder spaces without a weight is given. In an application, coercivity estimates in Holder norms for approximate solution of a nonlocal boundary value problem for elliptic-parabolic differential equation are obtained.

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

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 Holder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic-parabolic differential equations are obtained.