Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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.Article Citation - WoS: 20Citation - Scopus: 19A Highly Accurate Jacobi Collocation Algorithm for Systems of High-Order Linear Differential-Difference Equations With Mixed Initial Conditions(Wiley, 2015) Doha, E. H.; Baleanu, D.; Hafez, R. M.; Bhrawy, A. H.In this paper, a shifted Jacobi-Gauss collocation spectral algorithm is developed for solving numerically systems of high-order linear retarded and advanced differential-difference equations with variable coefficients subject to mixed initial conditions. The spatial collocation approximation is based upon the use of shifted Jacobi-Gauss interpolation nodes as collocation nodes. The system of differential-difference equations is reduced to a system of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The convergence is discussed graphically. The proposed method has an exponential convergence rate. The validity and effectiveness of the method are demonstrated by solving several numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier. Copyright (C) 2015 John Wiley & Sons, Ltd.Article Citation - WoS: 19Citation - Scopus: 18Efficient Jacobi-Gauss Collocation Method for Solving Initial Value Problems of Bratu Type(Pleiades Publishing inc, 2013) Bhrawy, A. H.; Baleanu, D.; Hafez, R. M.; Doha, E. H.In this paper, we propose the shifted Jacobi-Gauss collocation spectral method for solving initial value problems of Bratu type, which is widely applicable in fuel ignition of the combustion theory and heat transfer. The spatial approximation is based on shifted Jacobi polynomials J(n)((alpha, beta))(x) with alpha, beta is an element of (-1, infinity), x is an element of [0, 1] and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Illustrative examples have been discussed to demonstrate the validity and applicability of the proposed technique. Comparing the numerical results of the proposed method with some well-known results show that the method is efficient and gives excellent numerical results.Article Citation - WoS: 99Citation - Scopus: 110A New Jacobi Rational-Gauss Collocation Method for Numerical Solution of Generalized Pantograph Equations(Elsevier, 2014) Bhrawy, A. H.; Baleanu, D.; Hafez, R. M.; Doha, E. H.This paper is concerned with a generalization of a functional differential equation known as the pantograph equation which contains a linear functional argument. In this article, a new spectral collocation method is applied to solve the generalized pantograph equation with variable coefficients on a semi-infinite domain. This method is based on Jacobi rational functions and Gauss quadrature integration. The Jacobi rational-Gauss method reduces solving the generalized pantograph equation to a system of algebraic equations. Reasonable numerical results are obtained by selecting few Jacobi rational-Gauss collocation points. The proposed Jacobi rational-Gauss method is favorably compared with other methods. Numerical results demonstrate its accuracy, efficiency, and versatility on the half-line. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.