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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2010, 15(4), 709-719;

Symmetry Reduction and Numerical Solution of a Third-Order ODE from Thin Film Flow

Centre for Differential Equations, Continuum Mechanics and Applications School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa
Authors to whom correspondence should be addressed.
Published: 1 December 2010
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A new approach to solving high-order ordinary differential equations numerically is presented. Instead of the usual approach of writing a high-order ordinary differential equation as a system of first-order ordinary differential equations, we write the high-order ordinary differential equation in terms of its differential invariants. The third-order ordinary differential equation y′′′ = y−k for constant k is used to illustrate this approach for the cases k = 2 and k = 3.
Keywords: Thin film; third-order ODE; symmetry reduction Thin film; third-order ODE; symmetry reduction
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Momoniat, E.; Mahomed, F. Symmetry Reduction and Numerical Solution of a Third-Order ODE from Thin Film Flow. Math. Comput. Appl. 2010, 15, 709-719.

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