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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
mathematics
Hopscotch method: The numerical solution of the Frank-Kamenetskii partial differential equation
Applied Mathematics and Computation, Volume 217, No. 8, Year 2010
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Description
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. © 2010 Elsevier Inc. All rights reserved.
Authors & Co-Authors
Harley, Charis
South Africa, Johannesburg
University of the Witwatersrand
Statistics
Citations: 16
Authors: 1
Affiliations: 1
Identifiers
Doi:
10.1016/j.amc.2010.10.020
ISSN:
00963003