Browsing by Author "Dolapçi I.T."

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    Comparison of Approximate Symmetry Methods for Differential Equations
    (2004) Pakdemirli M.; Yürüsoy M.; Dolapçi I.T.
    Two current approximate symmetry methods and a modified new one are contrasted. Approximate symmetries of potential Burgers equation and non-Newtonian creeping flow equations are calculated using different methods. Approximate solutions corresponding to the approximate symmetries are derived for each method. Symmetries and solutions are compared and advantages and disadvantages of each method are discussed in detail.
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    Approximate symmetries of creeping flow equations of a second grade fluid
    (2004) Dolapçi I.T.; Pakdemirli M.
    Creeping flow equations of a second grade fluid are considered. Two current approximate symmetry methods and a modified new one are applied to the equations of motion. Approximate symmetries obtained by different methods and the exact symmetries are contrasted. Approximate solutions corresponding to the approximate symmetries are derived for each method. Symmetries and solutions are compared and advantages and disadvantages of each method are discussed in detail. © 2004 Elsevier Ltd. All rights reserved.
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    Symmetries and approximate solution of energy transfer equations in short pulse laser heating
    (2007) Pakdemirli M.; Dolapçi I.T.; Yilbaş B.S.
    Energy transfer equations in laser heating are considered. Symmetries of the equations are calculated by Lie Group theory. Using the symmetries, the equations are transferred to an ordinary differential system. Equations are approximately solved by strained parameter method, a perturbation technique. A boundary value problem in which the laser beam transfers heat to the surface is treated. Closed form approximate solutions for electron and lattice site temperature rise are obtained for a solid layer heated at the surface with a time decaying intensity pulse. Analytical solutions are verified by numerical simulations. © 2006 Elsevier Masson SAS. All rights reserved.
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    Analytical solution for non-equilibrium energy transfer in gold: Influence of ballistic contribution of electrons on energy transfer
    (2009) Yilbas B.S.; Dolapçi I.T.; Pakdemirli M.
    The analytical solution for non-equilibrium energy transfers in gold substrate and ballistic contribution of electrons to the energy transfer mechanism is examined. The non-equilibrium energy equation including the ballistic contribution of electrons is obtained using the electron kinetic theory approach. The analytical solution using the perturbation method is introduced to formulate lattice and electron temperature distributions in the film. A numerical method using the finite difference scheme is employed to predict and compare electron and lattice site temperatures to those obtained from the analytical solution. It is found that temperature remains high in the surface region of the gold film due to the cases: (i) accounting for the ballistic contribution of electrons to non-equilibrium energy transfer, and (ii) excluding the ballistic contribution to the non-equilibrium energy transfer. This is true for electron and lattice temperatures. Crown Copyright © 2008.
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    Application of pert urbation-iteration method to Lotka-Volterra equations
    (Elsevier B.V., 2016) Aksoy Y.; Göktaş U.; Pakdemirli M.; Dolapçi I.T.
    Perturbation-iteration method is generalized for systems of first order differential equations. Approximate solutions of Lotka-Volterra systems are obtained using the method. Comparisons of our results with each other and with numerical solutions are given. The method is implemented in Mathematica, a major computer algebra system. The package PerturbationIteration.m automatically carries out the tedious calculations of the method. © 2016 Faculty of Engineering, Alexandria University.