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## Nonlinear Systems of Equations

The solution of nonlinear systems of equations is an important problem in engineering. Applications include identifying the multiple steady states of a reactor network, predicting the azeotropes formed in a nonideal mixture, finding the steady-states of a flowsheet, and identifying equilibrium points in multiphase systems.

### Section 1: Literature Problems

 Test Problem Description AMPL File AMPL File 1 Himmelblau function HNE14.1.1.mod 2 Equilibrium Combustion HNE14.1.2.mod 3 Bullard-Biegler (1991) HNE14.1.3.mod 4 Ferraris-Tronconi (1986) HNE14.1.4.mod 5 Brown's almost linear system HNE14.1.5.mod 6 Robot kinematics problem HNE14.1.6.mod 7 Circuit design problem HNE14.1.7.mod 8 Steady state of a series of CSTRs with recycle HNE14.1.8.mod ex14.1.8.dat 9 Steady state temperatures of a nonisothermal CSTR HNE14.1.9.mod

### Section 2: Locating All Homogeneous Azeotropes

 Test Problem Description AMPLModel File AMPL Data File 1 Wilson equation - 3 component ex14.2.1.mod ex14.2.1.dat 2 Wilson equation - 4 component ex14.2.2.mod ex14.2.2.dat 3 Wilson equation - 5 component ex14.2.3.mod ex14.2.3.dat 4 NRTL equation - 3 component ex14.2.4.mod ex14.2.4.dat 5 NRTL equation - 4 component ex14.2.5.mod ex14.2.5.dat 6 UNIQUAC equation - 3 component ex14.2.6.mod ex14.2.6.dat 7 UNIQUAC equation - 4 component ex14.2.7.mod ex14.2.7.dat 8 UNIFAC equation - 3 component ex14.2.8.mod ex14.2.8.dat 9 UNIFAC equation - 4 component ex14.2.9.mod ex14.2.9.dat