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Yayınlar
- MakaleAçık Erişim2014High order of accuracy difference schemes for the inverse elliptic problem with Dirichlet condition
Ashyralyyev, Charyyar
The overdetermination problem for elliptic differential equation with Dirichlet boundary condition is considered. The third and fourth orders of accuracy stable difference schemes for the solution of this inverse problem are presented. Stability, almost coercive stability, and coercive inequalities for the solutions of difference problems are established. As a result of the application of established abstract theorems, we get well-posedness of high order difference schemes of the inverse problem for a multidimensional elliptic equation. The theoretical statements are supported by a numerical example.
- MakaleAçık Erişim2014On some geometric properties of a new paranormed sequence space
Karakaya, Vatan; Altun, Fatma
We introduce a new sequence space which is defined by the operator W=(wnk) on the sequence space ℓ(p). We define a modular functional on this space and investigate structure of this space equipped with Luxemburg norm. Also we study some geometric properties which are called Kadec-Klee, k-NUC, and uniform Opial properties and prove that this new space possesses these properties.
- MakaleAçık Erişim2014R-modified crank-nicholson difference scheme for fractional parabolic pde
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.
- DergiJournal of Function Spaces