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Design and Analysis of NSFD Methods for the Diffusion-Free Brusselator

Abstract:

This chapter reports on the design and analysis of two non-standard finite-
difference (NSFD) methods for solving the diffusion-free Brusselator system. The first NSFD
method is simulated using two different denominator functions. It is shown that, under certain
conditions, the first method exhibits spurious behaviour, such as failing to capture the correct
asymptotic stability properties of the unique fixed-point as well as the stable limit cycle of the
continuous-time diffusion-free Brusselator system. On the other hand, the second NSFD method, designed using a semi-exact discretization framework of Mickens, is shown to be elementary stable and dynamically consistent with the diffusion-free Brusselator system for sufficiently small timesteps. These theoretical results are illustrated via numerical simulations.

Authors: Andrew Kroshko, Oluwaseun Sharomi, Abba B Gumel, Raymond J Spiteri

Link: Here