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2011•Mathematical Problems in EngineeringOpen access

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

A. H. Bhrawy, Waleed Mohamed Abd-Elhameed

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Gauss, Collocation (remote sensing), Orthogonal collocation, Collocation method, Mathematics, Nonlinear system, Jacobi method, Spectral method

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