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- BildiriYalnız künye2012Finite difference method for the reverse parabolic problem with Neumann condition
Ashyralyyev, Charyyar; Dural, Ayfer; Sozen, Yasar; Ashyralyev, A; Lukashov, A
A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Neumann condition is applied. Stability, almost coercive stability, and coercive stability estimates for the solution of the first and second orders of accuracy difference schemes are obtained. The theoretical statements are supported by the numerical example.
- 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.
- 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.