Yazar "Bahadir, Ahmet Refik" seçeneğine göre listele

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    A Fully Implicit Finite Difference Approach for Numerical Solution of the Generalized Equal Width (GEW) Equation
    (Natl Acad Sciences India, 2020) Inan, Bilge; Bahadir, Ahmet Refik
    In this paper, a fully implicit finite difference method is presented to solve the generalized equal width equation. This implicit method allows to handle any values of p. Since the equation is nonlinear the scheme leads to a system of nonlinear equations. At each time step, Newton's method is used to solve this nonlinear system. The linear stability analysis of the proposed method is investigated using von Neumann approach and at the end of this investigation is seen that the method is unconditionally stable. The results are comparisons with analytical and other numerical values clearly show that results obtained using the fully implicit finite difference scheme are precise and reliable.
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    A numerical approach to hydromagnetic squeezed flow and heat transfer between two parallel disks
    (Emerald Group Publishing Ltd, 2011) Bahadir, Ahmet Refik; Abbasov, Teymuraz
    Purpose - The paper aims to investigate the effect of the electromagnetic field on the convective events which occur when electrically conducting fluid is squeezed between two parallel disks. Design/methodology/approach - The effects of the current occurring due to the direct voltage power supply at the thin electrical conducting fluid layer squeezed between the parallel disks, the magnetic field inducted by this current, and Ohmic heating on the squeezing process and heat convection are considered. Both approximate analytical and numerical solutions of the problem are obtained and a good agreement is observed between them. Findings - The effects of the basic parameters such as Hartmann number, Reynolds number, the ratio of the distance between the disks to the radius of the disks, Prandtl number, Eckert number, heat conduction, and electric current on the squeezing event, and load capacity of the fluid between two parallel disks are able to be determined from the solutions. These solutions also enable the effects of the basic parameters such as Hartmann number, Reynolds number, the ratio of the distance between the disks to the radius of the disks, Prandtl number, Eckert number, heat conduction, and electric current on the squeezing event and load capacity of the fluid between two parallel disks to be determined. Originality/value - Some important results and comparisons are presented graphically.
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    Numerical solution of the one-dimensional Burgers' equation: Implicit and fully implicit exponential finite difference methods
    (Indian Acad Sciences, 2013) Inan, Bilge; Bahadir, Ahmet Refik
    This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers' equation. As the Burgers' equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton's method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.
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    Numerical Solutions of MRLW Equation by a Fully Implicit Finite-Difference Scheme
    (Journal Mathematics & Computer Science-Jmcs, 2015) Inan, Bilge; Bahadir, Ahmet Refik
    In the present paper, a fully implicit finite difference method is introduced for the numerical solution of the modified regularized long wave (MRLW) equation. The accuracy of the method is examined by different problems of the MRLW equation. The results and comparisons with analytical and other numerical invariants clearly show that results obtained using the fully implicit finite difference scheme are precise and reliable.