Browsing by Author "Dolapci I.T."

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    Some exact solutions to the generalized Korteweg-de Vries equation and the system of shallow water wave equations
    (Vilnius University Press, 2013) Dolapci I.T.; Yildirim A.
    In this paper, we establish exact solutions for nonlinear evolution equations in mathematical physics. The exp-transform method is proposed to seek solitary solutions, periodic solutions and compaction-like solutions of nonlinear differential equations. The generalized KdV equation and the system of the shallow water wave equation are chosen to illustrate the effectiveness and convenience of the method. © Vilnius University, 2013.
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    New perturbation-iteration solutions of singular Emden-Fowler equations
    (Cambridge Scientific Publishers, 2022) Dolapci I.T.; Pakdemirli M.
    The new perturbation-iteration algorithm which has been applied previously to first order equations and Bratu type equations is implemented for solving singular Emden-Fowler differential equations. The simplest iteration algorithm is used and it is shown that the series solutions of this method produces compatible solutions with the exact solutions © CSP - Cambridge, UK; I&S - Florida, USA, 2022
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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.