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

E. Momoniat; F.M. Mahomed

doi:10.3390/mca15040709

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1 December 2010

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

and

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

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Math. Comput. Appl.2010, 15(4), 709-719;https://doi.org/10.3390/mca15040709

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Abstract

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

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