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

Author(s)
Khadijah M. Abualnaja

Affiliation(s)

Department of Mathematics and Statistics, College of Science, Taif University, Taif, Saudi Arabia.

Department of Mathematics and Statistics, College of Science, Taif University, Taif, Saudi Arabia.

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.

In this article, we derive a block procedure for some K-step linear multi-step methods (for

Keywords

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

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

Cite this paper

Abualnaja, K. (2015) A Block Procedure with Linear Multi-Step Methods Using Legendre Polynomials for Solving ODEs.*Applied Mathematics*, **6**, 717-723. doi: 10.4236/am.2015.64067.

Abualnaja, K. (2015) A Block Procedure with Linear Multi-Step Methods Using Legendre Polynomials for Solving ODEs.

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