Using bifurcation branches in complex domain to get multiple solutions

Authors:
Saeed Khaleghi;Farhang Jalali
Affiliations:
University of Tehran, Tehran, Iran;University of Tehran, Tehran, Iran
Venue:
CA '07 Proceedings of the Ninth IASTED International Conference on Control and Applications
Year:
2007

Citing 3
Cited 0

A Generic Global Optimization Algorithmfor the Chemical and Phase EquilibriumProblem

Journal of Global Optimization
Local bifurcation theory for multiparameter nonlinear eigenvalue problems

Nonlinear Analysis: Theory, Methods & Applications
Computational algebra for bifurcation theory

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.