A Differential Homotopy Continuation Method for Interlinked Solvent Extraction Cascades

Abstract

A robust differential homotopy procedure is developed that is suitable for solving the bordered block tridiagonal systems of nonlinear equations that result from liquid-liquid extraction models. The procedure is capable of readily utilizing newton, fixed-point, and custom homotopy mapping. It is shown to have an efficiency far superior to Kubicek's method and comparable to that of Rheinboldt. Application of the method to liquid-liquid extraction cascade models revealed that the newton homotopy would converge to a solution as rapidly as a simultaneous correction procedure and that use of a custom homotopy resulted in faster convercrence.