Yazar "Yildiz, S." seçeneğine göre listele

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    Öğe
    Approximation via Statistical Convergence in the Sense of Power Series Method of Bogel-Type Continuous Functions
    (Maik Nauka/Interperiodica/Springer, 2022) Demirci, K.; Yildiz, S.; Dirik, F.
    In this paper, we study Korovkin-type approximation for double sequences of positive linear operators defined on the space of all real valued B-continuous functions via the notion of statistical convergence in the sense of power series methods instead of Pringsheim convergence.We present an interesting application that satisfies our new approximation theorem which wasn'tsatisfied the one studied before. In addition, we derive the rate of convergence of the proposed approximation theorem. Finally, we give a conclusion for periodic functions.
  • [ X ]
    Öğe
    Energy preserving reduced-order modeling of the rotating thermal shallow water equation
    (Aip Publishing, 2022) Karasozen, B.; Yildiz, S.; Uzunca, M.
    In this paper, reduced-order models (ROMs) are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with state-dependent Poisson matrix. The high fidelity full solutions are obtained by discretizing the RTSWE in space with skew-symmetric finite-differences, while preserving the Hamiltonian structure. The resulting skew-gradient system is integrated in time by the energy preserving average vector field (AVF) method. The ROM is constructed by applying proper orthogonal decomposition with the Galerkin projection, preserving the reduced skew-gradient structure, and integrating in time with the AVF method. The nonlinear terms of the Poisson matrix and Hamiltonian are approximated with the discrete empirical interpolation method to reduce the computational cost. The solutions of the resulting linear-quadratic reduced system are accelerated by the use of tensor techniques. The accuracy and computational efficiency of the ROMs are demonstrated for a numerical test problem. Preservation of the energy (Hamiltonian) and other conserved quantities, i.e., mass, buoyancy, and total vorticity, show that the reduced-order solutions ensure the long-term stability of the solutions while exhibiting several orders of magnitude computational speedup over the full-order model. Furthermore, we show that the ROMs are able to accurately predict the test and training data and capture the system behavior in the prediction phase. Published under an exclusive license by AIP Publishing.