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**New algorithm for the numerical solutions of nonlinear third-order differential equations using Jacobi-Gauss collocation method.**
*(English)*
Zbl 1217.65155

Summary: 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.

### MSC:

65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

### Keywords:

algorithm; nonlinear third-order differential equation; Jacobi-Gauss collocation spectral method; numerical examples### Software:

Matlab
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\textit{A. H. Bhrawy} and \textit{W. M. Abd-Elhameed}, Math. Probl. Eng. 2011, Article ID 837218, 14 p. (2011; Zbl 1217.65155)

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