Khader, M.M. and Sweilam, N.H. (2013) On the Approximate Solutions for System of Fractional Integro-Differential Equations Using Chebyshev Pseudo-Spectral Method. Applied Mathematical Modelling, 37, 9819-9828.
http://dx.doi.org/10.1016/j.apm.2013.06.010

has been cited by the following article:

• TITLE: A Block Procedure with Linear Multi-Step Methods Using Legendre Polynomials for Solving ODEs

  AUTHORS: Khadijah M. Abualnaja

  KEYWORDS: Collocation Methods with Legendre Polynomials, Initial Value Problems, Perturbation Function, Fourth-Order Runge-Kutta Method

  JOURNAL NAME: Applied Mathematics, Vol.6 No.4, April 29, 2015

  ABSTRACT: In this article, we derive a block procedure for some K-step linear multi-step methods (for K = 1, 2 and 3), using Legendre polynomials as the basis functions. We give discrete methods used in block and implement it for solving the non-stiff initial value problems, being the continuous interpolant derived and collocated at grid and off-grid points. Numerical examples of ordinary differential equations (ODEs) are solved using the proposed methods to show the validity and the accuracy of the introduced algorithms. A comparison with fourth-order Runge-Kutta method is given. The ob-tained numerical results reveal that the proposed method is efficient.