Modification of the Regula Falsi method to accelerate system convergence in the prediction of trace quantities of atmospheric pollutants

Abstract

The Regula Falsi method is applied to prediction of trace quantities of air pollutants produced by combustion reactions such as those found in industrial point sources. Equilibrium quantities of uncombusted fuel generally are quite small, due to the exothermic nature of combustion reactions. Accordingly, calculating the maximum theoretical efficiency which may be achieved in a combustion process is difficult since the equations describing the equilibrium state are stiff. After reducing the system to that of one equation and one unknown, the Regula Falsi method may be applied in its modified form. The Regula Falsi method is modified through the introduction of an under-interpolation factor, which accelerates convergence of the numerical procedure in a manner similar to the Marquardt method of successive over-relaxation (SOR). Analogously, such a modification of the Regula Falsi method is referred to in this work as successive under-interpolation (SUI). Results indicate an excellent correlation between the under-interpolation factor and the number of iterations required to converge upon a solution.