Browsing by Author "Elmas, N"

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    APPROXIMATE DETERMINATION OF POLYNOMIAL ROOTS
    Pakdemirli, M; Sari, G; Elmas, N
    Three theorems are given for approximate determination of magnitudes of polynomial roots. A definition for the order of a number is given first. The first theorem is for a polynomial equation with all coefficients the same order of magnitude. The second theorem deals with polynomial equations having only one coefficient of different magnitude from the others. Finally, the third theorem is a general theorem valid for any arbitrary polynomial equations. The theorems successfully determine the magnitudes of roots for arbitrary degree of polynomial equations. An additional fourth theorem predicts the roots for the special case of two dominant terms in the polynomial. Proofs and numerical applications of each theorem are presented. It is shown that the predictions of the theorems and the real roots are in reasonable agreement.
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    Perturbation theorems for estimating magnitudes of roots of polynomials
    Pakdemirli, M; Elmas, N
    Two additional new theorems are posed and proven to estimate the magnitudes of roots of polynomials. Perturbation theory and the order of magnitude of terms are employed to develop the theorems. The theorems may be useful to estimate the order of magnitudes of the roots of a polynomial a priori before solving the equation. The theorems are developed for two special classes of polynomials of arbitrary order with their coefficients satisfying certain conditions. Numerical applications of the theorems are presented as examples. It is shown that the theorems produce good estimates for the magnitudes of roots. (C) 2010 Elsevier Inc. All rights reserved.
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    A new perturbation technique in solution of nonlinear differential equations by using variable transformation
    Elmas, N; Boyaci, H
    A perturbation algorithm using a new variable transformation is introduced. This transformation enables control of the independent variable of the problem. The problems are solved with new transformation: Classical Duffing equation with cubic nonlinear term and a singular perturbation problem. Results of multiple scales, Lindstedt Poincare method, new method and numerical solutions are contrasted. (C) 2013 Elsevier Inc. All rights reserved.