Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 37Citation - Scopus: 45The Operational Matrix Formulation of the Jacobi Tau Approximation for Space Fractional Diffusion Equation(Springer, 2014) Bhrawy, Ali H.; Baleanu, Dumitru; Ezz-Eldien, Samer S.; Doha, Eid H.In this article, an accurate and efficient numerical method is presented for solving the space-fractional order diffusion equation (SFDE). Jacobi polynomials are used to approximate the solution of the equation as a base of the tau spectral method which is based on the Jacobi operational matrices of fractional derivative and integration. The main advantage of this method is based upon reducing the nonlinear partial differential equation into a system of algebraic equations in the expansion coefficient of the solution. In order to test the accuracy and efficiency of our method, the solutions of the examples presented are introduced in the form of tables to make a comparison with those obtained by other methods and with the exact solutions easy.Article Citation - WoS: 24Citation - Scopus: 22Shifted Jacobi Spectral Collocation Method With Convergence Analysis for Solving Integro-Differential Equations and System of Integro-Differential Equations(inst Mathematics & informatics, 2019) Abdelkawy, Mohamed A.; Amin, Ahmed Z. M.; Baleanu, Dumitru; Doha, Eid H.This article addresses the solution of multi-dimensional integro-differential equations (IDEs) by means of the spectral collocation method and taking the advantage of the properties of shifted Jacobi polynomials. The applicability and accuracy of the present technique have been examined by the given numerical examples in this paper. By means of these numerical examples, we ensure that the present technique is simple and very accurate. Furthermore, an error analysis is performed to verify the correctness and feasibility of the proposed method when solving IDE.