A TRAJECTORY-FOLLOWING METHOD FOR SOLVING THE STEADY STATE OF CHEMICAL REACTION RATE EQUATIONS

Abstract

This article gives a trajectory-following method for the steady state of chemical reaction rate equations. In order to avoid wasting unnecessary computing time during the steady-state phase and get roughly accurate solutions during the transient-state phase, this method is realized via adopting the semi-implicit Euler formula as the stepping direction and adaptively adjusting the time-step size by an analogous trust-region technique. Under some standard assumptions, its global convergence analysis and local superlinear convergence analysis are also given. Finally, some numerical experiments of this method, in comparison with the traditional optimization methods and ordinary differential equation methods, are reported. The numerical results show that this trajectory-following method is a promising solution for this class of problems.