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- MakaleAçık Erişim2021On fourth order accuracy stable difference scheme for a multi-point overdetermined elliptic problem
Ashyralyyev, C.; Akyuz, G.
In this paper fourth order of accuracy difference scheme for approximate solution of a multi-point elliptic overdetermined problem in a Hilbert space is proposed. The existence and uniqueness of the solution of the difference scheme are obtained by using the functional operator approach. Stability, almost coercive stability, and coercive stability estimates for the solution of difference scheme are established. These theoretical results can be applied to construct a stable highly accurate difference scheme for approximate solution of multi point overdetermined boundary value problem for multidimensional elliptic partial differential equations.
- MakaleAçık Erişim2018Some approximations of second order derivatives complex-valued functions
Ashyralyyev, Ch; Ozturk, B.
In this paper, we generalize the well known finite difference method to compute derivatives of real valued function to approximate of second order complex derivatives w(zz) and w((zz) over bar) for complex-valued function w. Exploring different combinations of terms, we derive several approximations to compute the second order derivatives of complex-valued function. Several second order of accuracy finite differences to calculate derivatives are proposed. Error analysis in test examples is carried out by using Matlab program.