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- BildiriYalnız künye2016Stability estimates for solution of IBVP to fractional parabolic differential and difference equations
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.
- MakaleYalnız künye2014Scopus SJRQ3Well-posedness of fractional parabolic differential and difference equations with Dirichlet-Neumann conditions
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.
AtıfScopus12WoS6İncele - BildiriYalnız künye2014A note on fractional parabolic differential and difference equations
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.
AtıfScopus5WoS3OpenAlex4İncele - MakaleAçık Erişim2013Scopus SJRQ2FDM for fractional parabolic equations with the Neumann condition
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.
AtıfScopus20WoS16OpenAlex20İncele - BildiriYalnız künye2012Fractional parabolic differential and difference equations with the Dirichlet-Neumann condition
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.
AtıfScopus2WoS1OpenAlex1İncele - BildiriYalnız künye2011Stable difference schemes for fractional parabolic PDE
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.
AtıfScopus6WoS6OpenAlex1İncele