Mathematics / Matematik

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 9
    Citation - Scopus: 8
    Taylor Wavelets Collocation Technique for Solving Fractional Nonlinear Singular Pdes
    (Springer, 2022) Aghazadeh, Nasser; Mohammadi, Amir; Tanoğlu, Gamze
    A novel technique has been introduced to solve the Emden-Fowler equations. It has been derived from the Taylor wavelets collocation method. The proposed scheme has been successfully implemented in order to solve the singular equations. The singular problem converts to a system of algebraic equations that can be solved numerically. Moreover, the technique is very effective to remove the strong singularity point at x = 0. The numerical experiments have been checked out with the exact and approximate solutions that have been achieved by others including the Adomian decomposition method (Wazwaz in Appl Math Comput 166:638-651, 2005), Modified Homotopy Perturbation Method (Singh et al. J Math Chem 54(4):918-931, 2016). Also, the error analysis of the technique has been considered.
  • Article
    A Reliable and Fast Mesh-Free Solver for the Telegraph Equation
    (Springer, 2022) İmamoğlu Karabaş, Neslişah; Korkut, Sıla Övgü; Gürarslan, Gürhan; Tanoğlu, Gamze
    In the presented study, the hyperbolic telegraph equation is taken as the focus point. To solve such an equation, an accurate, reliable, and efficient method has been proposed. The developed method is mainly based on the combination of a kind of mesh-free method and an adaptive method. Multiquadric radial basis function mesh-free method is considered on spatial domain and the adaptive fifth-order Runge–Kutta method is used on time domain. The validity and the performance of the proposed method have been checked on several test problems. The approximate solutions are compared with the exact solution, it is shown that the proposed method has more preferable to the other methods in the literature.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    Integral Characteristics by Keyspace Partitioning
    (Springer, 2022) Demirbaş, Fatih; Kara, Orhun
    In this work, we introduce a new method we call integral by keyspace partitioning to construct integral characteristics for some block ciphers by introducing new integral properties. We introduce the concepts of active with constant difference and identically active integral properties. Then, we divide the key space into equivalence classes and construct integral characteristics for each equivalence class individually by using these integral properties. We exploit the binary diffusion layer and key schedule algorithm of a block cipher to propagate these integral properties through rounds. We apply the new method to the Byte-oriented Substitution-Permutation Network (BSPN) cipher and Midori64 to show its effectiveness. We construct the first iterative integral characteristic for a block cipher to the best of our knowledge. We extend this iterative characteristic for the (M, n)-(BSPN) block cipher where each block of BSPN contains M number of n× n S-Boxes with the block and key sizes M· n. Using at most (M-12)+1 (only 106 when M= 16) chosen plaintexts, we mount key recovery attacks for the first time on BSPN and recover the key for the full round. The time complexity of the key recovery is almost independent of the number of rounds. We also use our method to construct an integral characteristic for Midori64, which can be utilized for a key recovery attack on 11-round Midori64. Our results impose a new security criteria for the design of the key schedule algorithm for some block ciphers.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    A Reliable Explicit Method To Approximate the General Type of the Kdv–burgers’ Equation
    (Springer, 2022) Korkut, Sıla Övgü; İmamoğlu Karabaş, Neslişah
    This study aims to propose a reliable, accurate, and efficient numerical approximation for a general compelling partial differential equation including nonlinearity (uδ∂u∂x), dissipation (∂2u∂x2), and dispersion (∂3u∂x3) which arises in many fields of engineering as well as applied sciences. The novel proposed method has been developed combining a kind of mesh-free method called the Taylor wavelet method with the Euler method. The convergence result of the method has been presented theoretically. Moreover, the validation and applicability of the method have been also confirmed computationally on benchmark problems such as KdV–Burgers’ equation and modified-KdV equation. The numerical results have been compared both to the exact solution and to those in the existing literature. All presented figures and tables guarantee that the proposed method is highly accurate, efficient, and compatible with the nature of the specified equation physically. Furthermore, the recorded errors are evidence that the proposed method is the best approximation compared to those in the existing methods.