Applied Mathematics

Volume 6, Issue 4 (April 2015)

ISSN Print: 2152-7385   ISSN Online: 2152-7393

Google-based Impact Factor: 0.58  Citations  

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

HTML  XML Download Download as PDF (Size: 639KB)  PP. 717-723  
DOI: 10.4236/am.2015.64067    3,098 Downloads   4,500 Views  Citations

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.

Share and Cite:

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.

Cited by

[1] Numerical solution of stiff and oscillatory problems using third derivative trigonometrically fitted block method
Journal of the Nigerian …, 2022
[2] A three-step interpolation technique with perturbation term for direct solution of third-order ordinary differential equations
FUDMA JOURNAL OF …, 2021
[3] A Block Integrator for the Solution of First order Ordinary Differential Equations Using Legendre Polynomial
Asian Journal of Pure …, 2021
[4] A THREE-STEP INTERPOLATION TECHNIQUE WITH PERTURBATION TERM FOR DIRECT SOLUTION OF THIRD-ORDER ORDINARY DIFFERENTIAL …
2021
[5] Block Procedure for Solving Stiff First Order Initial Value Problems Using Chebyshev Polynomials
2020
[6] A Four-step Collocation Procedure by means of Perturbation term with Application to Third-order Ordinary Differential Equation
International Journal of Computer Applications, 2020
[7] Block procedure for solving stiff initial value problems using probabilists Hermite polynomials
2020
[8] A Seven-Step Block Multistep Method for the Solution of First Order Stiff Differential Equations
2020
[9] MODIFIED LAGUERRE COLLOCATION BLOCK METHOD FOR SOLVING SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS
2020
[10] Galerkin-FEM for obtaining the numerical solution of the linear fractional Klein–Gordon equation
J. Appl. Anal. Comput, 2019
[11] The Use of Adomian Decomposition Method in Solving Second Order Autonomous and Non-autonomous Ordinary Differential Equations
International Journal of Mathematics and Statistics Invention, 2019
[12] Numerical Study for System of ODEs Obtained from MHD Flow Past a Permeable Flat Plate in a Darcian Porous Medium Using Laguerre Collocation Method
2019
[13] Galerkin-FEM for obtaining the numerical solution of the linear fractional Klein-Gordon equation
2019
[14] BLOCK PROCEDURE WITH IMPLICIT SIXTH ORDER LINEAR MULTISTEP METHOD USING LEGENDRE POLYNOMIALS FOR SOLVING STIFF INITIAL VALUE PROBLEMS
Journal of Fundamental and Applied Sciences, 2019
[15] Three-Step Block Method for Solving Second Order Differential Equations
2018
[16] Convergence Properties of p (th) Order Diagonally Implicit Block Backward Differentiation Formulas
2018
[17] Modified Laguerre Collocation Block Method for Solving Initial Value Problems of First Order Ordinary Differential Equations
2018
[18] Convergence Properties of pth Order Diagonally Implicit Block Backward Differentiation Formulas
2018
[19] Numerical Approach for Solving Stiff Differential Equations Through the Extended Trapezoidal Rule Formulae
2017
[20] Continuous Hybrid Multistep Methods with Legendre Basis Function for Direct Treatment of Second Order Stiff ODEs
American J. of Computational and Applied Mathematics, 2016
[21] A computational solution of the multi-term nonlinear ODEs with variable coefficients using the integral-collocation-approach based on Legendre polynomials
2016
[22] Analytical and exact solutions of a certain class of coupled nonlinear PDEs using Adomian–Pade'method
2016
[23] Collocation approximation methods for solving higher-order ordinary differential equations
[24] Engineering and Applied Science Letter Vol. 3 (2020), Issue 3, pp. 20–29

Journals Menu
Follow SCIRP
Contact us
+1 323-425-8868
customer@scirp.org
WhatsApp +86 18163351462(WhatsApp)
Click here to send a message to me 1655362766
Paper Publishing WeChat

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.