Time-step-size-independent conditioning and sensitivity to perturbations in the numerical solution of index three differential algebraic equations

CARLO BOTTASSO; OLIVIER BAUCHAU; ALBERTO CARDONA

SIAM JOURNAL ON SCIENTIFIC COMPUTING

SIAM

Año: 2007 vol. 29 p. 397 - 414

1064-8275

We propose a simple preconditioning for the equations of motion of constrainedmechanical systems in index three form. The scaling transformation is applied to the displacement velocity-multiplier and to the reduced displacement-multiplier forms. The analysis of the transformed system shows that conditioning and sensitivity to perturbations become independent of the time stepsize, as in the case of well-behaved ordinary differential equations. The new scaling transformation issimple to implement and does not require the rewriting of the system equations as other approachesdo. The theoretical analysis is confirmed by numerical examples.