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Yayınlar
- MakaleAçık Erişim2022On the second order of accuracy stable difference scheme for integral type non-local elliptic source identification problem
Ashyralyyev, Charyyar
In this study, a source identification problem for elliptic differential equation with integral type non-local condition is discussed. The second order of accuracy difference scheme for elliptic non-local source identification problem is studied. Using spectral resolution of a self-adjoint operator, stability and coercive stability estimates for solution of difference scheme are established. Subsequently, difference scheme for an approximate solution of multi-dimensional boundary-value problem with integral type non-local and first kind boundary conditions is investigated for stability. Numerical results for 2D and 3D examples are illustrated.
- MakaleAçık Erişim2021Crank-nicolson difference scheme for reverse parabolic nonlocal problem with integral and neumann boundary conditions
Ashyralyyev, Charyyar; G¨onenc¸, Ahmet
In this paper, we study Crank-Nicholson difference scheme for approximate solutions of parabolic nonlocal reverse problem with integral and Neumann boundary conditions. Stability estimates for its solution are established. Via Mathlab framework, we give numerical example with explanation on computer realization.
- MakaleAçık Erişim2020The second order of ADS for reverse parabolic boundary value problem with integral condition
Ashyralyyev, Charyyar
Finite difference method to solve nonlocal reverse parabolic (RP) problem with integral condition are applied. The second order of accuracy difference scheme (ADS) for approximation of RP problem is proposed. Stability estimates (SEs) for solutions of this difference scheme (DS) are proved. Later, we propose the second order of ADS for approximation of multidimensional RP boundary value problem (BVP) with first kind boundary condition (BC) and establish SEs for its solu-tion. Numerical illustration for simple test problems is given.
- MakaleYalnız künye2020Stability of Rothe difference scheme for the reverse parabolic problem with integral boundary condition
Ashyralyyev, Charyyar
In this paper, we study the approximation of reverse parabolic problem with integral boundary condition. The Rothe difference scheme for an approximate solution of reverse problem is discussed. We establish stability and coercive stability estimates for the solution of the Rothe difference scheme. In sequel, we investigate the first order of accuracy difference scheme for approximation of boundary value problem for multidimensional reverse parabolic equation and obtain stability estimates for its solution. Finally, we give numerical results together with an explanation on the realization in one- and two-dimensional test examples.