Abstract
This paper is devoted to the hopscotch scheme, which is a numerical integration technique for time-dependent partial differential equations. We examine its linear stability properties. A general theorem is presented which provides sufficient conditions for boundedness of the numerical solution during time stepping on a fixed space-time mesh. This theorem has applications in the field of parabolic problems. For the one-space-dimensional convection-diffusion equation we present a detailed stability analysis of the odd-even scheme combined with central and one-sided finite differences. We compare stability based on the spectral condition with von Neumann stability.
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