Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Department: search.filters.department.İzmir Institute of TechnologyInstitution Author: search.filters.institutionAuthor.Aghazadeh, Nasser

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Now showing 1 - 4 of 4
  • Article
    A Chebyshev Wavelet Approach to the Generalized Time-Fractional Burgers-Fisher Equation
    (Univ Tabriz, 2025) Aghazadeh, Nasser
    This work proposes a new method for obtaining the approximate solution of the time-fractional generalized BurgersFisher equation. The method's main idea is based on converting the nonlinear partial differential equation to a linear partial differential equation using the Picard iteration method. Then, the second kind Chebyshev wavelet collocation method is used to solve the linear equation obtained in the previous step. The technique is called the Chebyshev Wavelet Picard Method (CWPM). The proposed method successfully solves the time fractional generalized Burgers-Fisher equation. The obtained numerical results are compared with the exact solutions and with the solutions obtained using the Haar wavelet Picard method and the homotopy perturbation method.
  • Article
    Citation - Scopus: 1
    A Finite Difference Approach To Solve the Nonlinear Model of Electro-Osmotic Flow in Nano-Channels
    (University of Tabriz, 2025) Aghazadeh, N.; Rabbani, K.; Otaghsara, S.H.T.; Rabbani, M.
    This article considers a system of coupled equations constructed by the nonlinear model of electro-osmotic flow through a one-dimensional nano-channel. Functions that belong to this system include distributions of mole fraction of cation and anion, electrical potential, and velocity. We try to find an accurate closed-form solution. To this end, some mathematical approaches are concurrently used to convert the equations to a nonlinear differential equation in terms of the mole fraction of anion. The latter nonlinear differential equation is transformed into a nonlinear algebraic system by the finite difference method, and the system’s solution is obtained using Newton’s iterative algorithm. Furthermore, equations for the mole fraction of cation, electrical potential, and velocity in terms of the mole fraction of anion are obtained. We calculate errors by substituting the proposed solution into the equations to validate the results. Comparing the results with some other numerical research works demonstrates an acceptable accuracy. © 2025 Elsevier B.V., All rights reserved.
  • Article
    An Efficient Chebyshev Wavelet Collocation Technique for the Time-Fractional Camassa-Holm Equation
    (World Scientific Publ Co Pte Ltd, 2025) Aghazadeh, Nasser
    By employing the third-order Chebyshev collocation technique along with relevant wavelets, we tackle a third-order singular fractional partial differential equation (PDE). We directly build the Chebyshev operation matrix of the third kind, avoiding the use of the block-pulse function or any approximations. To reduce the order of equation in this approach, we transform the higher-order PDEs into a system of PDEs. Next, we utilize the third-kind Chebyshev wavelet collocation method to convert the resulting system from the prior step into a set of algebraic equations. To demonstrate the method's effectiveness, we apply it to the time-fractional Camassa-Holm equation and a third-order time-singular PDE. The outcomes are compared with those from several established methods to illustrate the method's efficiency and practicality.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 8
    A Numerical Method Based on Legendre Wavelet and Quasilinearization Technique for Fractional Lane-Emden Type Equations
    (Springer, 2024) İdiz, F.; Tanoǧlu, G.; Aghazadeh, N.
    In this research, we study the numerical solution of fractional Lane-Emden type equations, which emerge mainly in astrophysics applications. We propose a numerical approach making use of Legendre wavelets and the quasilinearization technique. The nonlinear term in fractional Lane-Emden type equations is iteratively linearized using the quasilinearization technique. The linearized equations are then solved using the Legendre wavelet collocation method. The proposed method is quite effective to overcome the singularity in fractional Lane-Emden type equations. Convergence and error analysis of the proposed method are given. We solve some test problems to compare the effectiveness of the proposed method with some other numerical methods in the literature. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.