A global fixed-point homotopy has not found wide application in chemical engineering for solving systems of nonlinear equations by continuation. Rather, the Newton and problem-dependent homotopies have been favored. However, it is conjectured here that the fixed-point homotopy would be expected to always place all real roots of the system on a global homotopy path because the path is forced to begin from a single starting point. If so, all roots could be computed by following the single path with a suitable continuation method. This would be particularly desirable when the number of real roots to a system cannot be predetermined and one wishes to compute all solutions. In this study, it was found that such a path does exist provided that a criterion is used for selecting a starting point which minimizes the number of real roots of the global fixed-point homotopy function at an infinite value of the homotopy parameter. Several examples, including an adiabatic reactor with multiple solutions are presented to illustrate the application of the criterion. While methods have been devised recently to find all roots of polynomial equations, this is the first method for systematically locating all roots to general systems of nonlinear equations.The necessity of solving systems of nonlinear equations often arises in simulating and designing a chemical plant or optimizing a process. Newton's method or Powell's method are commonly applied to solve such systems. However, as described by Seader (1985), both methods have well-known disadvantages such as the requirement * Author to whom all correspondence should be addressed. Present address: Daitec Co., Ltd., 4-85 Chikara-machi Higashi-ku Nagoya-shi, Japan. Minoru Kuno was on leave from Daitec Co., Ltd., during the course of the study reported here.
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