Matrix Exponentiation and the Frank-Kamenetskii Equation

Author:

Momoniat E.1

Affiliation:

1. 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

Abstract

Long time solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a vessel are obtained using matrix exponentiation. Spatial derivatives are approximated by high-order finite difference approximations. A forward difference approximation to the time derivative leads to a Lawson-Euler scheme. Computations performed with a BDF approximation to the time derivative and a fourth-order Runge-Kutta approximation to the time derivative are compared to results obtained with the Lawson-Euler scheme. Variation in the central temperature of the vessel corresponding to changes in the shape parameter and Frank-Kamenetskii parameter are computed and discussed.

Funder

National Research Foundation

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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