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Öğe The Comparative Boubaker Polynomials Expansion Scheme (BPES) and Homotopy Perturbation Method (HPM) for solving a standard nonlinear second-order boundary value problem(Pergamon-Elsevier Science Ltd, 2011) Kocak, H.; Yildirim, A.; Zhang, D. H.; Mohyud-Din, S. T.In this paper, we propose an analytical solution to a nonlinear second-order boundary value problem using the Homotopy Perturbation Method (HPM) and the 4q-Boubaker Polynomials Expansion Scheme (BPES). Both methods have been applied to a particular differential problem. The results are plotted, and compared with exact solutions proposed elsewhere, in order to evaluate accuracy. (C) 2011 Elsevier Ltd. All rights reserved.Öğe A MORE APPROXIMATE GREEN'S FUNCTION FOR THE ELECTRIC FIELD VECTOR WITH ANISOTROPIC PROPERTIES(Taylor & Francis Ltd, 2012) Yildirim, A.; Kocak, H.In this study, approximate Green's functions for a vector equation for the electric field with anisotropic dielectric permittivity and magnetic permeability is obtained by means of homotopy perturbation method (HPM). The HPM deforms the nonlinear partial differential equations to a system of manageable partial differential equations. These systems become amenable to analytical solutions which have been expressed in the form of an infinite power series. The results reveal that the proposed method is very effective and simple and can be applied to other nonlinear problems.Öğe A range-free method to determine antoine vapor-pressure heat transfer-related equation coefficients using the Boubaker polynomial expansion scheme(Maik Nauka/Interperiodica/Springer, 2011) Kocak, H.; Dahong, Z.; Yildirim, A.In this study, a range-free method is proposed in order to determine the Antoine constants for a given material (salicylic acid). The advantage of this method is mainly yielding analytical expressions which fit different temperature ranges.Öğe A SECOND ATTEMPT TO ESTABLISH AN ANALYTICAL EXPRESSION TO STEAM-WATER DIPOLE ORIENTATION PARAMETER USING THE BOUBAKER POLYNOMIALS EXPANSION SCHEME(Pleiades Publishing Inc, 2011) Yue, W. X.; Kocak, H.; Zhang, D. H.; Yildirim, A.In this paper, an analytical expression to the steam-water dipole orientation parameter is proposed. The calculations have been carried out under the presumptions that: the electric properties of the water molecules are characterized completely by a permanent dipole moment and a constant scalar polarizability, that translational fluctuations may be neglected, and that the positions are orientation-free. The results are presented in the form of continuous and integrable expressions that can be easily compared to the precedent studies as well as involved in similar analytical models.
