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Hirayama, H. (2000) Arbitrary Order and A-Stable Numerical Method for Solving Algebraic Ordinary Differential Equation by Power Series. 2nd International Conference on Mathematics and Computers in Physics, Vouliagmeni, Athens, 9-16 July 2000, 1-6.

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.