Long time solutions to the Frank-Kamenetskii partial differential equation modelling athermal explosion in a vessel are obtained using matrix exponentiation. Spatial derivativesare approximated by high-order finite difference approximations. A forward differenceapproximation to the time derivative leads to a Lawson-Euler scheme. Computationsperformed 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 theLawson-Euler scheme. Variation in the central temperature of the vessel correspondingto changes in the shape parameter and Frank-Kamenetskii parameter are computed anddiscussed.
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