Ashyralyev, Allaberen; Ashyralyyev, Charyyar; Cakalli, H.; Kocinac, L.D.R.; Ashyralyev, A.; Harte, R.; Dik, M.; Canak, I.; Kandemir, H.S.; Tez, M.

In this work, we study time-nonlocal boundary value problem for multi-dimensional parabolic partial differential equation. Two difference schemes for approximate solution of non-local boundary value problem are discussed. Theorems on stability of solutions both difference schemes are given without proof. Numerical results for test examples are outlined.

Ashyralyev, Allaberen; Al-Hammouri, Ahmad; Ashyralyyev, Charyyar

The present paper is devoted to study the first order of accuracy absolute stable difference scheme for the approximate solution of the space identification problem for the elliptic-telegraph equation in Hilbert spaces with the self-adjoint positive definite operator. The main theorem on the stability of the difference scheme is established. In applications, theorems on the stability of difference schemes for two types of the space identification problems for multidimensional elliptic-telegraph partial differential equations are proved. Numerical analysis is provided.

Ashyralyev, Allaberen; Ashyralyyev, Charyyar; Zvyagin, Viktor G.; Ashyralyev, A.; Ashralyyev, C.; Erdogan, A.S.; Lukashov, A.; Sadybekov, M.

We study the well-posedness of the source identification problem for the two dimensional elliptic differential equation with nonlocal boundary conditions. Applying operator approaches, the exact estimates for the solution of this problem in Hölder norms are established.

Ashyralyev, Allaberen; Ashyralyyev, Charyyar; Cakalli, H.; Kocinac, L.D.R.; Harte, R.; Cavalcanti, V.N.D.; Ashyralyev, A.; Sakalli, I.; Canak, I.; Gurtug, O.

Ashyralyev, Allaberen; Cakir, Zafer; Lukashov, A.; Ashyralyev, A.

In this work, we investigate initial-boundary value problems for fractional parabolic equations with the Neumann boundary condition. Stability estimates for the solution of this problem are established. Difference schemes for approximate solution of initial-boundary value problem are constructed. Furthermore, we give theorem on coercive stability estimates for the solution of the difference schemes.

Ashyralyev, Allaberen; Emirov, Nazar; Cakir, Zafer

We study initial-boundary value problems for fractional parabolic equations with the Dirichlet-Neumann conditions. We obtain a stable difference schemes for this problem, and obtain theorems on coercive stability estimates for the solution of the first order of accuracy difference scheme. A procedure of modified Gauss elimination method is applied for the solution of the first and second order of accuracy difference schemes of one-dimensional fractional parabolic differential equations.

Ashyralyev, Allaberen; Ashyralyyev, Charyyar

The boundary value problem of determining the parameter of an elliptic equation -u(t) + Au(t) = f(t) + p (0 ≤ t ≤ T), u(0) = φ, u(T) = ψ u(λ) = ξ 0 < λ < T, with a positive operator A in an arbitrary Banach space E is studied. The exact estimates are obtained for the solution of this problem in Hölder norms. Coercive stability estimates for the solution of boundary value problems for multi-dimensional elliptic equations are established.

Ashyralyev, Allaberen; Cakir, Zafer

The second order of accuracy stable difference scheme for the numerical solution of the mixed problem for the fractional parabolic equation are presented using by r-modified Crank-Nicholson difference scheme. Stability estimate for the solution of this difference scheme is obtained. A procedure of modified Gauss elimination method is used for solving this difference scheme in the case of one-dimensional fractional parabolic partial differential equations. Numerical results for this scheme and the Crank-Nicholson scheme are compared in test examples.

Ashyralyev, Allaberen; Artykov, Merdan; Cakir, Zafer; Ashyralyev, A; Malkowsky, E

In this work, the first and second order of difference schemes that approximately solve the initial-boundary value problem for multidimensional fractional parabolic equation with Dirichlet boundary condition are presented. The stability estimates for the solution of these difference schemes are established.

Ashyralyev, Allaberen; Cakir, Zafer

In the present study, the first and second order of accuracy stable difference schemes for the numerical solution of the initial boundary value problem for the fractional parabolic equation with the Neumann boundary condition are presented. Almost coercive stability estimates for the solution of these difference schemes are obtained. The method is illustrated by numerical examples.

Ashyralyev, Allaberen; Cakir, Zafer

The first and second order of accuracy stable difference schemes for the numerical solution of the mixed problem for the fractional parabolic equation are presented. Stability and almost coercive stability estimates for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of one-dimensional fractional parabolic partial differential equations.

Ashyralyev, Allaberen; Emirov, Nazar; Cakir, Zafer; Ashyralyev, A; Lukashov, A

The multidimensional fractional parabolic equation with the Dirichlet-Neumann condition is studied. Stability estimates for the solution of the initial-boundary value problem for this fractional parabolic equation are established. The stable difference schemes for this problem are presented. Stability estimates for the solution of the first order of accuracy difference scheme are obtained. A procedure of modified Gauss elimination method is applied for the solution of first and second order of accuracy difference schemes of one-dimensional fractional parabolic differential equations.

Ashyralyev, Allaberen; Cakir, Zafer; Simos, TE

The stable difference schemes for the multidimensional fractional parabolic equation with Dirichlet and Neumann boundary conditions are presented. Stability estimates and almost coercive stability estimates with ln 1/τ+|h| for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes of one-dimensional fractional parabolic partial differential equations.