BIT Numerical Mathematics

, Volume 38, Issue 4, pp 663–673

# Highest order multistep formula for solving index-2 differential-algebraic equations

• Yang Cao
• Qingyang Li
Article

## Abstract

In this paper, the maximum order of linear multistep methods (LMM) for solving semi-explict index-2 differential-algebraic equations (DAEs) is discussed. For ak-step formula, we prove that the orders of differential variables and algebraic variables do not exceedk+1 andk respectively whenk is odd and both orders do not exceedk whenk is even. In order to achieve the orderk+1, the coefficients in the formula should satisfy some strict conditions. Examples which can achieve the maximum order are given fork=1,2,3. Especially, a class of multistep formula fork=3, not appearing in the literature before, are proposed. Further, a class of predictor-corrector methods are constructed to remove the restriction of the infinite stability. They give the same maximum order as that for solving ODEs. Numerical tests confirm the theoretical results.

65L05

## Key words

Index-2 differential-algebraic equations maximum order linear multistep methods PECE methods

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