Abstract
The objectives of this paper are to investigate how various numerical treatments of the nonlinear source term in a model reaction-convection equation can affect the stability of steady-state numerical solutions and to show under what conditions the conventional linearized stability analysis breaks down. The symbiotic relationship between the strong dependence on initial data and the permissibility of spurious stable and unstable asymptotic numerical solutions for explicit and implicit treatment of the source terms are revealed and analyzed. It can be shown that nonlinear analysis uncovers much of the nonlinear phenomena which linearized analysis is not capable of predicting in a model reaction-convection equation.
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