WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article An Investigation of Discontinuities in Time-Dependent 2D and 3D Parabolic Partial Differential Equations Utilizing Collocation Methods: A Comparative Analysis of Complex Interface Problems(Springer Heidelberg, 2025) Faheem, Muhammad; Asif, Muhammad; Amin, Rohul; Haider, Nadeem; Jarad, FahdParabolic double interface problems have many applications in the fields such as materials science, fluid dynamics, and heat transfer. This paper presents a comparison of the Haar wavelet-based collocation method and two variants of radial basis function (RBF) method for solving 2D and 3D, linear as well as nonlinear, parabolic double interface problems. The two variants of RBF methods are the multiquadric RBF method and the integrated RBF method. For linear problems, the system of equations obtained from the integrated RBF method is solved using Moore-Penrose pseudoinverse. Error analysis is performed using L infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_\infty $$\end{document} norm error and root mean square error, and the findings are discussed in detail. The methods are compared based on their accuracy and efficiency in solving different benchmark problems. The results show that both the Haar wavelet collocation method and the integrated RBF method perform better than the conventional RBF method in terms of accuracy.Article Citation - WoS: 42Citation - Scopus: 50Mobile Language Learning: Contribution of Multimedia Messages Via Mobile Phones in Consolidating Vocabulary(Springer Heidelberg, 2012) Saran, Murat; Saran, Murat; Seferoglu, Golge; Cagiltay, Kursat; Bilgisayar MühendisliğiThis study aimed at investigating the effectiveness of using multimedia messages via mobile phones in helping language learners in consolidating vocabulary. The study followed a pre-test/post-test quasi-experimental research design. The participants of this study were a group of students attending the English Preparatory School of an English-medium university in Turkey. Six different groups were formed in order to investigate the comparative effectiveness of supplementary vocabulary materials delivered through three different means: via mobile phones, on web pages, and in print form. The multimedia messages in this study included the definitions of words, exemplary sentences, related visual representations, information on word formation, and pronunciations of words. Analyses of the quantitative data showed that using mobile phones had positive effects on students' vocabulary acquisition. The results suggest that mobile phones offer great potential for providing learners with supplementary opportunities to recontextualize, recycle, and consolidate vocabulary.Article Citation - WoS: 5Citation - Scopus: 4Robust Numerical Techniques for Modeling Telegraph Equations in Multi-Scale and Heterogeneous Environments(Springer Heidelberg, 2025) Asif, Muhammad; Bilal, Faisal; Haider, Nadeem; Jarad, FahdThe article presents an innovative concept called the hyperbolic telegraph interface model, which effectively integrates regular interfaces. This hybrid method leverages Haar wavelets in conjunction with the finite difference method to provide robust numerical solutions. It is expertly designed for both linear and nonlinear models, adeptly handling constant or variable coefficients across regular interfaces. At the heart of this technique is the approximation of spatial derivatives using truncated Haar series, while time derivatives are efficiently processed through the finite difference method. The methodology has been rigorously tested across a variety of linear and nonlinear models, demonstrating its effectiveness. In linear problems, the algebraic system is solved with precision using the Gauss elimination method. For nonlinear challenges, the Quasi-Newton linearization formula is applied to successfully eliminate non-linearity from the model. To evaluate the technique's performance, we analyze key metrics such as maximum absolute errors, root mean square errors, and computational convergence rates with varying numbers of collocation points. The proposed approach consistently outperforms existing methods, particularly in situations involving abrupt changes in the solution space or discontinuities between boundary and initial conditions, delivering stable solutions in these critical scenarios. The combination of strong theoretical foundations and computational stability, along with excellent convergence rates and comprehensive numerical studies, firmly validates the accuracy and versatility of this method, confirming its wide range of applications.Article Citation - WoS: 19Citation - Scopus: 18Innovative Stability Analysis of Complex Secondary Toppling Failures in Rock Slopes Using the Block Theory(Springer Heidelberg, 2025) Mao, Yimin; Azarafza, Mohammad; Bonab, Masoud Hajialilue; Pusatli, Tolga; Nanehkaran, Yaser A.We present the block theory-based secondary toppling stability analysis method (BTSTSA), an advanced and novel method specifically designed to assess secondary toppling failures in slopes. This innovative method comprehensively accounts for various failure mechanisms and computes the factor of safety (F.S) for rock slopes. Grounded in Block theory principles, particularly the key-block method, and supplemented by limit equilibrium techniques, BTSTSA offers a practical and reliable analytical framework. Our investigation focused on five discontinuous rock slopes in the South Pars region, southwest Iran, which are affected by composite toppling failure mechanisms. The stability analysis results were meticulously verified using the Aydan-Kawamoto method, a recognized benchmark in the field. Comparative analysis consistently demonstrated that the BTSTSA approach generates more conservative estimates of the F.S compared to the Aydan-Kawamoto method. This conservatism underscores the robustness and reliability of the BTSTSA framework and highlights its implications for practical engineering applications. The integration of this innovative analytical method with data from these investigations offers crucial insights for geotechnical engineers, equipping them to manage the complexities of secondary toppling failures in discontinuous rock slopes. These findings emphasize the importance of considering conservatism in engineering applications and provide a more accurate and reliable assessment of slope stability, particularly concerning secondary toppling failures, thereby benefiting geotechnical engineering practices.Article Citation - WoS: 29Citation - Scopus: 30Monic Chebyshev Pseudospectral Differentiation Matrices for Higher-Order Ivps and Bvps: Applications To Certain Types of Real-Life Problems(Springer Heidelberg, 2022) Abdelhakem, M.; Ahmed, A.; Baleanu, D.; El-kady, M.We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in differentiation matrices (D-matrices). Those matrices have been used to approximate the solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be used in this work. The first technique is a direct approximation of the H-ODE. While the second technique depends on transforming the H-ODE into a system of lower order ODEs. We discuss the error analysis of these D-matrices in-depth. Also, the approximation and truncation error convergence have been presented to improve the error analysis. Some numerical test functions and examples are illustrated to show the constructed D-matrices' efficiency and accuracy.Article Citation - WoS: 20Citation - Scopus: 20Bipolar Intuitionistic Fuzzy Graph Based Decision-Making Model To Identify Flood Vulnerable Region(Springer Heidelberg, 2023) Augustin, Felix; Narayanamoorthy, Samayan; Ahmadian, Ali; Balaenu, Dumitru; Kang, Daekook; Nithyanandham, DevaBipolar intuitionistic fuzzy graphs (BIFG) are an extension of fuzzy graphs that can effectively capture uncertain or imprecise information in various applications. In graph theory, the covering, matching, and domination problems are benchmark concepts applied to various domains. These concepts may not be defined precisely using a crisp graph when the vertices and edges are more uncertain. Therefore, this study defines the covering, matching and domination concepts in bipolar intuitionistic fuzzy graphs (BIFG) using effective edges with certain important results. To define these concepts when the effective edges are absent, some novel approaches are discussed. To illustrate the domination concepts, the applications in disaster management and location selection problems are discussed. Further, a BIFG-based decision-making model is designed to identify the flood-vulnerable zones in Chennai, where the city's most and least vulnerable zones are identified. From the proposed model, Kodambakkam (Z(10)) is the most susceptible zone in Chennai. Finally, a comparative analysis is done with the existing techniques to show the efficiency of the model.Article Citation - WoS: 9Citation - Scopus: 10Identifying the Source Function for Time Fractional Diffusion With Non-Local in Time Conditions(Springer Heidelberg, 2021) Baleanu, Dumitru; Agarwal, Ravi P.; Long, Le Dinh; Luc, Nguyen HoangThe diffusion equation has many applications in fields such as physics, environment, and fluid mechanics. In this paper, we consider the problem of identifying an unknown source for a time-fractional diffusion equation in a general bounded domain from the nonlocal integral condition. The problem is non-well-posed in the sense of Hadamard, i.e, if the problem has only one solution, the solution will not depend continuously on the input data. To get a stable solution and approximation, we need to offer the regularization methods. The first contribution to the paper is to provide a regularized solution using the modified fractional Landweber method. Two choices are proposed including a priori and a posteriori parameter choice rules, to estimate the convergence rate of the regularized methods. The second new contribution is to use truncation to give an estimate of L-p for the convergence rate.Article Citation - WoS: 33Citation - Scopus: 37Approximation of Fixed Point and Its Application To Fractional Differential Equation(Springer Heidelberg, 2021) Uddin, Izhar; Baleanu, Dumitru; Khatoon, SabiyaIn this study, we prove some convergence results for generalized alpha-Reich-Suzuki non-expansive mappings via a fast iterative scheme. We validate our result by constructing a numerical example. Also, we compare our results with the other well known iterative schemes. Finally, we calculate the approximate solution of nonlinear fractional differential equation.Article Citation - WoS: 19Citation - Scopus: 20An Inverse Source Problem for Pseudo-Parabolic Equation With Caputo Derivative(Springer Heidelberg, 2022) Luc, Nguyen Hoang; Tatar, Salih; Baleanu, Dumitru; Can, Nguyen Huu; Long, Le DinhIn this paper, we consider an inverse source problem for a fractional pseudo-parabolic equation. We show that the problem is severely ill-posed (in the sense of Hadamard) and the Tikhonov regularization method is proposed to solve the problem. In addition, we present numerical examples to illustrate applicability and accuracy of the proposed method to some extent.Article Citation - WoS: 13Citation - Scopus: 13A Taylor-Chebyshev Approximation Technique To Solve the 1d and 2d Nonlinear Burgers Equations(Springer Heidelberg, 2022) Yuzbasi, Suayip; Baleanu, Dumitru; Izadi, MohammadThis 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.