Improving the accuracy of BDF methods for index 3 dierential algebraic equations
Methods for solving index 3 DAEs based on BDFs suffer a loss of accuracy when there is a change of step size or a change of order of the method. A layer of nonuniform convergence is observed in these cases, and O(1) errors may appear in the algebraic variables. From the viewpoint of error control, it is beneficial to allow smooth changes of step size, and since most codes based on BDFs are of vari