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.
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    Perturbation substitution method for ordinary differential equations
    (Cambridge Scientific Publishers, 2025) Pakdemirli M.; Dolapci I.T.
    A new perturbation method is proposed. In addition to the perturbation series expansion of the dependent variable, the independent variable is also expanded as arbitrary functions. The arbitrary function expansions gives more flexibility in choosing the specific forms of the functions so that secular terms, small-divisor terms, blow-up terms which limit the validity of expansions can be eliminated. The method has the capability to produce a number of solutions ranging from regular perturbation solutions to even exact solutions if available. Several linear and nonlinear ordinary differential equation problems are treated with the new method. A boundary layer type problems is treated as well. The link between the new method and the other perturbation methods are outlined in the examples considered. The advantage of the new method is that it inherits more arbitrariness in the expansions so that many different approximate solutions including the regular solutions and even exact solutions can be constructed. The disadvantage is that the selection of the independent expansion functions is not straightforward and the solutions depend on the specific choices. © CSP - Cambridge, UK