Semi-implicit method for the solution of systems of stiff ordinary differential and differential-algebraic equations

Abstract

A new semi-implicit method, referred to as the R-V or reverse variable technique, has been developed for the solution of systems of ODEs and DAES. R-V owes its name to the portion of the method in which the dependent variables are incremented and the minimum time step which satisfies criteria on the increments is determined. The approach originated from the need to repeatedly integrate highly nonlinear kinetics equations to simulate countercurrent flow bleaching, extraction and washing systems for paper production. Conventional approaches were slow and often unreliable when applied to these systems. The R-V method proved very effective in accurately integrating the initial rapid phase and then rapidly stepping through the usually slow reaction phase. The purpose of the note is to describe the algorithm which extends the method to the solution of general systems of ODEs. The discussion includes advantages and characteristics as well as limitations of the method and applications to the solutions of DAEs, PDEs and roots of algebraic equations.