Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
2 results
Search Results
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: 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.