**On BDF-Based Multistep Schemes for Some Classes of Linear Differential-Algebraic Equations of Index at Most 2
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* Mikhail Valeryanovich Bulatov, Vu Hoang Linh, Liubov Stepanovna Solovarova *

**Abstract**

A family of efficient multistep difference schemes for solving some classes of linear non-autonomous differential-algebraic equations of index at most 2 is proposed. It is shown that if the popular backward differentiation formulas (BDFs) are applied to a reformulated form of the original problem, then the methods preserve the stability property and the convergence order that the corresponding BDF methods possess in the ODE case. Further issues such as numerical differentiation that may be involved in the implementation and computational errors are also discussed. Finally, several numerical experiments are given which confirm the theoretical results.