Symmetry reduction and numerical solution of a third-order ode from thin film flow

E. Momoniat; F. M. Mahomed

doi:10.3390/mca15040709

Symmetry reduction and numerical solution of a third-order ode from thin film flow

E. Momoniat, F. M. Mahomed

University of the Witwatersrand

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

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.

Original language	English
Pages (from-to)	709-719
Number of pages	11
Journal	Mathematical and Computational Applications
Volume	15
Issue number	4
DOIs	https://doi.org/10.3390/mca15040709
Publication status	Published - 2010
Externally published	Yes

Keywords

Symmetry reduction
Thin film
Third-order ODE

ASJC Scopus subject areas

General Engineering
Computational Mathematics
Applied Mathematics

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10.3390/mca15040709

Cite this

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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.",

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AU - Mahomed, F. M.

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AB - 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.

KW - Symmetry reduction

KW - Thin film

KW - Third-order ODE

UR - https://www.scopus.com/pages/publications/78650351386

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DO - 10.3390/mca15040709

M3 - Article

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ER -

Symmetry reduction and numerical solution of a third-order ode from thin film flow

Abstract

Keywords

ASJC Scopus subject areas

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