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Hopscotch method: The numerical solution of the Frank-Kamenetskii partial differential equation. (English) Zbl 1205.80086
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.

80M20Finite difference methods (thermodynamics)
80A20Heat and mass transfer, heat flow
35Q79PDEs in connection with classical thermodynamics and heat transfer
65M12Stability and convergence of numerical methods (IVP of PDE)
Full Text: DOI
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