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Browsing by Author "Ahmadian, A."

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    Article
    Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods
    (2020) Baleanu, Dumitru; Senu, N.; Ahmadian, A.; Ibrahim, S. N. I.; Baleanu, Dumitru; 56389
    This study introduces new special two-derivative Runge-Kutta type (STDRKT) methods involving the fourth derivative of the solution for solving third-order ordinary differential equa-tions. In this regards, rooted tree theory and the corresponding B-series theory is proposed to derive order conditions for STDRKT methods. Besides, explicit two-stages fifth order and three-stages sixth order STDRKT methods are derived and stability,consistency and convergence of STDRKT methods are analysed in details. Accuracy and effectiveness of the proposed techniques are vali-dated by a number of various test problems and compared to existing methods in the literature. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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    Article
    The generalized complex Ginzburg–Landau model and its dark and bright soliton solutions
    (2021) Baleanu, Dumitru; Mirzazadeh, M.; Baleanu, Dumitru; Raza, N.; Park, C.; Ahmadian, A.; Salahshour, S.; 56389
    In the present work, the generalized complex Ginzburg–Landau (GCGL) model is considered and its 1-soliton solutions involving different wave structures are retrieved through a series of newly well-organized methods. More exactly, after considering the GCGL model, its 1-soliton solutions are obtained using the exponential and Kudryashov methods in the presence of perturbation effects. As a case study, the effect of various parameter regimes on the dynamics of the dark and bright soliton solutions is analyzed in three- and two-dimensional postures. The validity of all the exact solutions presented in this study has been examined successfully through the use of the symbolic computation system.