Ali Baharev

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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)
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)
; 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)
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)
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)
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)