Matrix exponentiation and the frank-kamenetskii equation

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4 Citations (Scopus)


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.

Original languageEnglish
Article number713798
JournalMathematical Problems in Engineering
Publication statusPublished - 2012
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering


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