Matrix Exponentiation and the Frank-Kamenetskii Equation

E. Momoniat

Mathematical Problems in Engineering, 2012, vol. 2012, 1-14

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:713798

DOI: 10.1155/2012/713798

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