Solving a System of Nonlinear Algebraic Equations You Only Get Error Messages—What to do Next?


  • Mordechai Shacham Ben-Gurion University of the Negev • Beer-Sheva 84105, Israel
  • Neima Brauner Tel-Aviv University • Tel-Aviv 69978, Israel


Chemical engineering problems often involve the solution of systems of nonlinear algebraic equations (NLE). There are several software packages that can be used for solving NLE systems, but they may occasionally fail, especially in cases where the mathematical model contains discontinuities and/or regions where some of the functions are undefined. Here we describe and demonstrate the use of a systematic procedure for reformulating the NLE system so as to increase the probability of finding a solution and at the same time speeding up the solution process.

Author Biographies

Mordechai Shacham, Ben-Gurion University of the Negev • Beer-Sheva 84105, Israel

Mordechai Shacham is professor emeritus of the Department of Chemical Engineering at the Ben-Gurion University of the Negev in Israel. He served as department head and the chairman of the Israeli Inter-University Center for e-Learning (IUCEL). He received his B.Sc. and D.Sc. degrees from the Technion, Israel Institute of Technology. His research interest includes analysis, modeling, and regression of data; applied numerical methods; and prediction of physical properties.

Neima Brauner, Tel-Aviv University • Tel-Aviv 69978, Israel

Neima Brauner is currently a professor of mechanical engineering at Tel-Aviv University, School of Engineering. She received her B.Sc. and M.Sc. in chemical engineering from the Technion Institute of Technology in Haifa, and a Ph.D. in mechanical engineering from Tel-Aviv University in 1983. Her research interest includes hydrodynamics and transport phenomena in two-phase flow systems, and applications of interactive statistical and numerical methods in regression of experimental data, process analysis, and design.