Adaptive cellular integration of linearly implicit differential equations

The use of cell-to-cell mapping methods for the global analysis of linearly implicit ODEs is addressed in this paper. Limitations of simple and adjoining cell mapping when applied to linearly implicit equations motivate the introduction of a finite-time convergence model for cellular methods, which unifies time and spatial discretization with numerical aspects in a comprehensive framework. The resulting formal characterization of some properties of simple and adjoining cell mapping leads to a hybridization of both techniques, which is shown to be well-behaved for the analysis of linearly implicit ODEs.