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

• 作者: Khadijah M. Abualnaja
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: COLLOCATION Methods with LEGENDRE POLYNOMIALS Initial Value Problems Perturbation Function FOURTH-ORDER RUNGE-KUTTA Method
• 年，卷（期）: 2015,（4）
• 页码范围: 717-723
• 页数: 7页
• 分类号: O1

摘要

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.