A new index reduction algorithm for DAEs is developed. In the usual manner, parts of the DAE are differentiated analytically and appended to the original system. For each additional equation, a derivative is selected to be replaced by a new algebraic variable called a dummy derivative. The resulting augmented system is at most index 1, but no longer overdetermined. The dummy derivatives are not subject to discretization; their purpose is to annihilate part of the dynamics in the DAE, leaving only what corresponds to the dynamics of a state-space form. No constraint stabilization is necessary in the subsequent numerical treatment. Numerical tests indicate that the method yields results with an accuracy comparable to that obtained for the corresponding state-space ODE.

MSC codes

  1. 65L05


  1. differential-algebraic
  2. index reduction
  3. dummy derivative
  4. constraint stabilization
  5. solution invariant
  6. automatic differentiation

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: 677 - 692
ISSN (online): 1095-7197


Submitted: 10 July 1991
Accepted: 15 May 1992
Published online: 13 July 2006

MSC codes

  1. 65L05


  1. differential-algebraic
  2. index reduction
  3. dummy derivative
  4. constraint stabilization
  5. solution invariant
  6. automatic differentiation



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