| Description |
The homotopy continuation method is a state of the art numerical technique for solving systems of non-linear equations. In this study, HOMPACK, a suite of codes which use the homotopy method to create a globa"y convergent algorithm for solving systems of non-linear equations, was tested on a dibutyl-phthalate reactor design problem. Two of the basic methods available in HOMPACK, the fixed-point homotopy, and the polynomial solver, were tested on the problem. The fixed-point homotopy was divergent for the system of equations considered, but the polynomial solver was able to locate a" 48 roots of the system. To find the roots, 28,800 Jacobian evaluations were required resulting in 252 minutes of CPU time on the Unvivac 1100. Only one real positive solution to the problem was found. The other 47 roots were either complex or negative. The model indicates that a maximum of 7.820 Ibmoles/hr of dibutyl-phthalate can be produced in the described reactor system. |
