Browsing by Author "Izadi, Mohammad"

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Citation - WoS: 9
Citation - Scopus: 10
An Effective Qlm-Based Legendre Matrix Algorithm To Solve the Coupled System of Fractional-Order Lane-Emden Equations
(Elsevier, 2024) Baleanu, Dumitru; Izadi, Mohammad
The purpose of this study is to propose a computationally effective algorithm for the numerical evaluation of a fractional-order system of singular Lane -Emden type equations arising in physical problems. The fractional operator considered is in the sense of the Liouville-Caputo derivative. The presented matrix collocation method is based upon a combination of the quasilinearization method (QLM) and the shifted Legendre functions (SLFs) and is called QLM-SLFs method. By applying first the QLM to the nonlinear underlying system, we get a family of linear equations. Hence, a spectral matrix collocation scheme relied on the SLFs is designed to solve the resulting sequence of linear system of equations at very few iterations. The uniform convergence of the shifted Legendre expansion series solution is established. To illustrate the effectiveness of the proposed QLM-SLFs technique in the present paper, three test examples are carried out. The applicability and validity of the proposed method are testified through comparisons with the outcomes of other existing procedures in the literature. The proposed QLM-SLFs method is efficient and easy to implement. The approximation obtained by the method also converges quickly to the solutions of the underlying model problem. In comparison with available existing computational procedures, the QLM-SLFs approach shows that the use of Legendre functions together with QLM provides solutions with high accuracy and exponential convergence rate.
Citation - WoS: 13
Citation - Scopus: 13
A Taylor-Chebyshev Approximation Technique To Solve the 1d and 2d Nonlinear Burgers Equations
(Springer Heidelberg, 2022) Yuzbasi, Suayip; Baleanu, Dumitru; Izadi, Mohammad
This paper deals with proposing an approximate solution for the well-known Burgers equation as a canonical model of various fields of science and engineering. Our novel combined approximation algorithm is based on the linearized Taylor approach for the time discretization, while the spectral Chebyshev collocation method is utilized for the space variables. This implies that in each time step, the proposed combined approach reduces the one- and two-dimensional model problems into a system of linear equations, which consists of polynomial coefficients. The error analysis of the present approach in 1D and 2D is discussed. Through numerical simulations, the utility and efficiency of the combined scheme are examined and comparisons with exact solutions as well as existing available methods have been performed. The comparisons indicate that the combined approach is efficient, practical, and straightforward in implementation. The technique developed can be easily extended to other nonlinear models.