Using Bifurcation Branches in Complex Domain to Get Multiple Solutions

S. Khaleghi and F. Jalali (Iran)


Bifurcation, homotopy continuation, complex domain, and fixed-point homotopy.


Bifurcation branches through complex domain have been applied to locate all solutions of the most nonlinear problems in chemical engineering. When we use homotopy continuation method in real space, depend on initial guess only some of roots are traced by homotopy path. However, there are some turning points which converted to branching points using complex variables. Other roots are reached when we bifurcate from these points into the complex space. Some examples are presented to show how it can be done in solving nonlinear sets of equations, especially in phase equilibrium and stability problems which contain the most nonlinearity in process simulations.

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