Abstract :
The Implicit Euler method is seldom used to solve differential–algebraic equations (DAEs) of differential index r⩾3, since the method in general fails to converge in the first r−2 steps after a change of stepsize. However, if the differential equation is of order d=r−1⩾1, an alternative variable-step version of the Euler method can be shown uniformly convergent. For d=r−1, this variable-step method is equivalent to the Implicit Euler except for the first r−2 steps after a change of stepsize. Generalization to DAEs with differential equations of order d>r−1⩾1, and to variable-order formulas is discussed.
