Uniqueness of completions for linear time varying differential algebraic equations

Abstract The extent to which a completion x ′= G ( t ) x +∑ r i = 0 R i ( t ) f ( i ) ( t ) of a linear ti me varying differential algebraic equation E ( t ) x ′( t )+ F ( t ) x ( t )= f ( t ) is unique is carefully examined. The implications for numerical methods for solving DAEs based on differentiated equations are discussed.