Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 118Citation - Scopus: 125Numerical Simulation of Time Variable Fractional Order Mobile-Immobile Advection-Dispersion Model(Editura Acad Romane, 2015) Abdelkawy, M. A.; Baleanu, Dumitru; Zaky, M. A.; Bhrawy, A. H.; Baleanu, D.; MatematikThis paper reports a novel numerical technique for solving the time variable fractional order mobile-immobile advection-dispersion (TVFO-MIAD) model with the Coimbra variable time fractional derivative, which is preferable for modeling dynamical systems. The main advantage of the proposed method is that two different collocation schemes are investigated for both temporal and spatial discretizations of the TVFO-MIAD model. The problem with its boundary and initial conditions is then reduced to a system of algebraic equations that is far easier to be solved. Numerical results are consistent with the theoretical analysis and indicate the high accuracy and effectiveness of this algorithm.Article Citation - WoS: 13Citation - Scopus: 14An Accurate Legendre Collocation Scheme for Coupled Hyperbolic Equations With Variable Coefficients(Editura Acad Romane, 2014) Doha, E. H.; Baleanu, Dumitru; Bhrawy, A. H.; Baleanu, D.; Abdelkawy, M. A.; MatematikThe study of numerical solutions of nonlinear coupled hyperbolic partial differential equations (PDEs) with variable coefficients subject to initial-boundary conditions continues to be a major research area with widespread applications in modern physics and technology. One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (NPDEs) as well as PDEs with variable coefficients. A numerical solution based on a Legendre collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients. This approach, which is based on Legendre polynomials and Gauss-Lobatto quadrature integration, reduces the solving of nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equations that is far easier to solve. The obtained results show that the proposed numerical algorithm is efficient and very accurate.