Browsing by Publisher "Institute of Applied Mathematics of Baku State University"

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    APPROXIMATE DETERMINATION OF POLYNOMIAL ROOTS
    (Institute of Applied Mathematics of Baku State University, 2016) 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. © 2016, Institute of Applied Mathematics of Baku State University. All rights reserved.
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    NUMERICAL SOLUTION OF VOLTERRA SERIES WITH ERROR ESTIMATION
    (Institute of Applied Mathematics of Baku State University, 2022) Tari A.; Bildik N.
    In this paper, an important applied problem, namely Volterra series, is investigated. Here, the well-known differential transform (DT) method is extended to solve the multiple non-linear Volterra integral equations which lead to Volterra series. To this end, some basic properties of DT are given, then by proving some theorems, the DT method is extended to solve the mentioned equations. Next, a scheme to estimate the error of solution is proposed and the convergence of the method is proved. Finally, the validity and applicability of the proposed method is illustrated by some examples. © 2022, Institute of Applied Mathematics of Baku State University. All rights reserved.
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    FUNCTIONAL ROOT ALGORITHMS FOR TRANSCENDENTAL EQUATIONS
    (Institute of Applied Mathematics of Baku State University, 2024) Pakdemirli M.; Dolapci I.T.
    By employing tangent functions, a class of root-finding algorithms is generated in its most general form. Sample algorithms corresponding to special forms of the functions are given next. The functional algorithms involve only first order derivatives and are generalizations of the Newton-Raphson method with the same quadratic order of convergence. Some special functional algorithms employing second order derivatives are also presented with cubic order of convergence. The algorithms are numerically tested and compared with the Newton-Raphson method. The advantages and the disadvantages as well as some criteria on how to select a suitable function is discussed. It is shown that by selecting an appropriate functional form, the number of iterations can be reduced and/or range of convergence interval can be increased. © 2024, Institute of Applied Mathematics of Baku State University. All rights reserved.