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Multiple steady states are typically discovered by tracing a solution path, including turning points. A new technique is presented here that does not follow this approach. The original problem is solved directly, without tracing a solution path. The proposed branch and prune algorithm is guaranteed to find all solutions automatically. Core components of the… (More)

- Ali Baharev
- 2008

Computing the steady state of multistage counter-current processes like distillation, extraction, or absorption is the equivalent to finding solutions for large scale non-linear equation systems. The conventional solution techniques are fast and efficient if a good estimation is available but are prone to fail, and do not provide information about the… (More)

A method is proposed that either returns all solutions to steady-state models of distillation columns or proves infeasibility. No initial estimates are required. The computational effort grows linearly with the number of stages. Successful solution of a numerically challenging reactive distillation column with 7 steady-states show the robustness of the… (More)

The need of reliably solving systems of nonlinear equations often arises in the everyday practice of chemical engineering. In general, standard methods cannot provide theoretical guarantee for convergence to a solution, cannot reliably find multiple solutions, and cannot prove non-existence of solutions. Interval methods provide tools to overcome these… (More)

; and Sándor Kemény is professor at the same institution (email: kemeny@mail.bme.hu). The authors wish to thank Mr. Richárd Király for his preliminary work. The authors are grateful to the Associate Editor of STCO and the unknown reviewers for their helpful suggestions. 2 ABSTRACT AND KEY WORDS Unfortunately many of the numerous algorithms for computing the… (More)

- Ali Baharev, Endre Rév
- 2008

Solving general nonlinear systems of equations and/or finding the global optimum of nonconvex functions constitute an important part of the everyday practice in chemical engineering. Standard methods cannot provide theoretical guarantee for convergence to a solution, cannot find multiple solutions, and cannot prove non-existence of solutions. This is the… (More)

Interval arithmetic can be successfully applied to find all the solutions of systems of nonlinear equations in a given region with mathematical certainty. Not finding any solution means non-existence of solutions in the studied region. The mathematical certainty, provided by the method, makes interval arithmetic a powerful tool for solving problems from the… (More)

Chemical process models are highly structured. Information on how the hierarchical components are connected helps to solve the model efficiently. Our ultimate goal is to develop structure-driven optimization methods for solving nonlinear programming problems (NLP). The structural information retrieved from the JModelica environment will play an important… (More)

Tearing is a long-established decomposition technique, widely adapted across many engineering fields. It reduces the task of solving a large and sparse nonlinear system of equations to that of solving a sequence of low-dimensional ones. The most serious weakness of this approach is well-known: It may suffer from severe numerical instability. The present… (More)

This paper focuses on finding all solutions to nonlinear algebraic systems of equations in a given domain. First, scattered points are computed that can be considered as a representative sample of the solution manifold of a given underdetermined nonlinear system of equations. If this underdetermined system is then augmented by further equations such that… (More)