Matrix Exponentiation and the Frank-Kamenetskii Equation
2012 ◽
Vol 2012
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pp. 1-14
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Keyword(s):
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.
Keyword(s):
2008 ◽
Vol 24
(6)
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pp. 1371-1387
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Keyword(s):
2013 ◽
Vol 10
(02)
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pp. 1341001
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2017 ◽
2014 ◽
Vol 24
(14)
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pp. 2743-2783
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1987 ◽
Vol 14
(5)
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pp. 235-239
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Keyword(s):
2014 ◽
Vol 875-877
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pp. 781-785
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