Numerical solution of non-linear algebraic equations with discontinuities

Mordechai Shacham, Neima Brauner

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The solution of systems of non-linear algebraic equations with discontinuities in the solution search domain is considered. It is demonstrated that such problems are often very difficult to solve, even with the state of the art numerical solvers, and even when initial guesses close to the solutions are used. The application of constrained solution methods that do not require evaluation of function and derivative values outside of a predefined (feasible) subspace of the variables for solving such systems is considered. An algorithm is presented for identifying and handling of sub-expressions that introduce discontinuities. These are either removed by algebraic manipulations, or defined as boundaries of a feasible subspace. Using the proposed approach, it is demonstrated that a feasible solution for originally unsolvable problems can be found.

Original languageEnglish
Pages (from-to)1449-1457
Number of pages9
JournalComputers and Chemical Engineering
Issue number10
StatePublished - 15 Oct 2002


  • Constrained non-linear equations
  • Function discontinuity
  • Root finding

ASJC Scopus subject areas

  • General Chemical Engineering
  • Computer Science Applications


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