Completion to involution and semidiscretisations Original Research Article

We discuss the relation between the completion to involution of linear over-determined systems of partial differential equations with constant coefficients and the properties of differential algebraic equations obtained by their semidiscretisation. For a certain class of “weakly over-determined” systems, we show that the differential algebraic equations do not contain hidden constraints, if and only if the original partial differential system is involutive. We also demonstrate how the formal theory can be used to obtain an existence and uniqueness theorem for smooth solutions of strongly hyperbolic systems and to estimate the drift off the constraints, if an underlying equation is numerically solved. Finally, we show for general linear systems how the index of differential algebraic equations obtained by semidiscretisations can be predicted from the result of a completion of the partial differential system.