Extensions of the HHT-α method to differential-algebraic equations in mechanics

Laurent O. Jay and Dan Negrut

Abstract

We present second order extensions of the Hilber-Hughes-Taylor-$\alpha$ (HHT-$\alpha$) method for systems of overdetermined differential-algebraic equations (ODAEs) arising, for example, in mechanics. A detailed analysis of extensions of the HHT-$\alpha$ method is given. In particular a local and global error analysis is presented. Second order convergence is theoretically demonstrated and practically illustrated by numerical experiments. A new variable stepsize formula is proposed which preserves the second order of the method.

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Key words

differential-algebraic equations, HHT-$\alpha$ method, variable stepsize

AMS subject classifications

65L05, 65L06, 65L80, 70F20, 70H45

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