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Zbl 1205.80086
Harley, C.
Hopscotch method: The numerical solution of the Frank-Kamenetskii partial differential equation. (English)
[J] Appl. Math. Comput. 217, No. 8, 4065-4075 (2010). ISSN 0096-3003

Summary: Numerical solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a cylindrical vessel are obtained using the hopscotch scheme. We observe that a nonlinear source term in the equation leads to numerical difficulty and hence adjust the scheme to accommodate such a term. Numerical solutions obtained via MATLAB, MATHEMATICA and the Crank-Nicolson implicit scheme are employed as a means of comparison. To gain insight into the accuracy of the hopscotch scheme the solution is compared to a power series solution obtained via the Lie group method. The numerical solution is also observed to converge to a well-known steady state solution. A linear stability analysis is performed to validate the stability of the results obtained.

MSC 2000:: *80M20 Finite difference methods
80A20 Heat and mass transfer
35Q79
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: hopscotch scheme; thermal explosion; nonlinear source term; linear stability analysis

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	Scientific prize winners of the ICM 2010
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	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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Zentralblatt MATH Berlin [Germany]