On the solution of differential-algebraic equations through gradient flow embedding

Ehecatl Antonio del Rio-Chanona, Craig Bakker, Fabio Fiorelli, Michail Paraskevopoulos, Felipe Scott, Raúl Conejeros, Vassilios S. Vassiliadis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper Gradient Flow methods are used to solve systems of differential-algebraic equations via a novel reformulation strategy, focusing on the solution of index-1 differential-algebraic equation systems. A reformulation is first effected on semi-explicit index-1 differential-algebraic equation systems, which casts them as pure ordinary differential equation systems subject to an embedded pointwise least-squares problem. This is then formulated as a gradient flow optimization problem. Rigorous proofs for this novel scheme are provided for asymptotic and epsilon convergence. The computational results validate the predictions of the effectiveness of the proposed approach, with efficient and accurate solutions obtained for the case studies considered. Beyond the theoretical and practical value for the solution of DAE systems as pure ODE ones, the methodology is expected to have an impact in similar cases where an ODE system is subjected to algebraic constraints, such as the Hamiltonian necessary conditions of optimality in optimal control problems.

Translated title of the contributionSobre la solución de ecuaciones algebraicas diferenciales mediante incrustación de flujo en gradiente
Original languageEnglish
Pages (from-to)165-175
Number of pages11
JournalComputers and Chemical Engineering
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Ltd


  • DAE
  • Differential-algebraic equations
  • Gradient flow
  • Ordinary differential equations
  • Semi-explicit index-1


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