New Algorithm for the Numerical Solutions of Nonlinear Third-Order Differential Equations Using Jacobi-Gauss Collocation Method-Reference-Cited by-同舟云学术

New Algorithm for the Numerical Solutions of Nonlinear Third-Order Differential Equations Using Jacobi-Gauss Collocation Method

Published:2011 Issue: Volume:2011 Page:1-14
ISSN:1024-123X
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Bhrawy A. H.¹²^ORCID,Abd-Elhameed W. M.³^ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

2. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

3. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

Abstract

A new algorithm for solving the general nonlinear third-order differential equation is developed by means of a shifted Jacobi-Gauss collocation spectral method. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithm, and some comparisons are made with the existing results. The method is easy to implement and yields very accurate results.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2011/837218.pdf

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2. Approximate solution of a differential equation arising in astrophysics using the variational iteration method

3. An approximation algorithm for the solution of the nonlinear Lane–Emden type equations arising in astrophysics using Hermite functions collocation method

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