Yazar "Işık, Osman Raşit" için listeleme
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Analysis of second order and unconditionally stable BDF2-AB2 method for the Navier-Stokes equations with nonlinear time relaxation
Işık, Osman Raşit; Yüksel, Gamze; Demir, Bülent (Wiley, 2018)In this study, we first consider a second order time stepping finite element BDF2-AB2 method for Navier-Stokes equations (NSE). We prove that the method is unconditionally stable and O(Delta t(2)) accurate. Second, we ... -
Bernstein Collocation Method for Solving MHD Jeffery-Hamel Blood Flow Problem with Error Estimations
Bataineh, Ahmad Sami; Işık, Osman Raşit; Hashim, Ishak (HINDAWI LTD, 2022)n this paper, the Bernstein collocation method (BCM) is used for the first time to solve the nonlinear magnetohydrodynamics (MHD) Jeffery-Hamel arterial blood flow issue. The flow model described by nonlinear partial ... -
Bernstein method for the MHD flow and heat transfer of a second grade fluid in a channel with porous wall
Bataineh, A. Sami; Işık, Osman Raşit; Hashim, I. (Elsevier Science Inc, 2016)In this paper, we present an approximate solution method for the problem of magnetohydrodynamic (MHD) flow and heat transfer of a second grade fluid in a channel with a porous wall. The method is based on the Bernstein ... -
Bernstein Series Solution of a Class of Lane-Emden Type Equations
Işık, Osman Raşit; Sezer, Mehmet (Hindawi Ltd, 2013)The purpose of this study is to present an approximate solution that depends on collocation points and Bernstein polynomials for a class of Lane-Emden type equations with mixed conditions. The method is given with some ... -
An Enhanced Adaptive Bernstein Collocation Method for Solving Systems of ODEs
Bataineh, Ahmad Sami; Işık, Osman Raşit; Oqielat, Moa’ath; Hashim, Ishak (MDPI, 2021)In this paper, we introduce two new methods to solve systems of ordinary differential equations. The first method is constituted of the generalized Bernstein functions, which are obtained by Bernstein polynomials, and ... -
Error analysis of the Chebyshev collocation method for linear second-order partial differential equations
Yüksel, Gamze; Işık, Osman Raşit; Sezer, Mehmet (Taylor & Francis Ltd, 2015)The purpose of this study is to apply the Chebyshev collocation method to linear second-order partial differential equations (PDEs) under the most general conditions. The method is given with a priori error estimate which ... -
Fractional bernstein series solution of fractional diffusion equations with error estimate
Alshbool, Mohammed Hamed; Işık, Osman Raşit; Hashim, Ishak (MDPI, 2021)In the present paper, we introduce the fractional Bernstein series solution (FBSS) to solve the fractional diffusion equation, which is a generalization of the classical diffusion equation. The Bernstein polynomial method ... -
Multistage Bernstein collocation method for solving strongly nonlinear damped systems
Bataineh, Ahmad Sami; Al-Omari, Abd Alkreem; Işık, Osman Raşit; Hashim, Ishak (Sage Publications Ltd, 2019)In this paper, we propose an approximate solution method, called multistage Bernstein collocation method (MBCM), to solve strongly nonlinear damped systems. The method is given with an error analysis. The systems investigated ... -
Numerical analysis of Backward-Euler discretization for simplified magnetohydrodynamic flows
Yüksel, Gamze; Işık, Osman Raşit (Elsevier Science Inc, 2015)Magnetohydrodynamics (MHD) studies consider the dynamics of electrically conducting fluids. MHD are described by a set of equations, which are a combination of the Navier-Stokes equations of fluid dynamics and Maxwell's ... -
A numerical approach based on Bernstein collocation method: Application to differential Lyapunov and Sylvester matrix equations
Sadek, Lakhlifa; Bataineh, Ahmad Sami; Işık, Osman Raşit; Alaoui, Hamad Talibi; Hashim, Ishak (Elsevier B.V., 2023)In this paper, we apply the Bernstein collocation method to construct the solution set of the Sylvester matrix differential equation (Sy-MDE) which involves the Lyapunov matrix differential equation. The method depends on ... -
A numerical method to solve fractional pantograph differential equations with residual error analysis
Gökmen, Elçin; Işık, Osman Raşit (SPRINGER HEIDELBERG, 2021)In this study, we have introduced a fractional series solution method to solve fractional pantograph differential equations numerically. The method is constructed by collocation approach and Bernstein polynomials. Each ... -
Second order time relaxation model for accelerating convergence to steady-state equilibrium for Navier-Stokes equations
Işık, Osman Raşit; Takhirov, Aziz; Zheng, Haibiao (Elsevier Science Bv, 2017)This paper deals with the problem of accelerating convergence to equilibrium for the Navier-Stokes equation using time relaxation models. We show that the BDF2 based semidiscrete solution of the regularized scheme converges ... -
Solution of fractional-order differential equations based on the operational matrices of new fractional Bernstein functions
Alshbool, M. H. T.; Bataineh, A. S.; Hashim, I.; Işık, Osman Raşit (Elsevier, 2017)An algorithm for approximating solutions to fractional differential equations (FDEs) in a modified new Bernstein polynomial basis is introduced. Writing x -> x(alpha) (0 < alpha < 1) in the operational matrices of Bernstein ... -
Taylor collocation approach for delayed Lotka-Volterra predator-prey system
Gökmen, Elçin; Işık, Osman Raşit; Sezer, Mehmet (Elsevier Science Inc, 2015)In this study, a numerical approach is proposed to obtain approximate solutions of the system of nonlinear delay differential equations defining Lotka-Volterra prey predator model. By using the Taylor polynomials and ...
