A Note on High/Low-Wave-Number Interactions in Spatially Discrete Parabolic Equations

Abstract

We describe an instability introduced by the spatial discretization of reaction-diffusion equations. The mechanism is a nonlinear interaction between high and low wave-number modes in the discrete equations. In partial differential equations which exhibit strong temporal growth, a parasitic high-wave-number mode is stimulated, through aliasing, by a physically meaningful low-wave-number mode. We analyse the interaction using phase-plane techniques and present complementary numerical results.

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