AMPLITUDE-SHAPE METHOD FOR THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

Abstract

The numerical solution of large stiff systems of ordinary differential equations is very expensive and often impossible to be done on a PC. Even if a large mainframe computer is used, it might be too slow to follow the evolution of a physical system in real time and parallel computations are needed. In this paper we propose an amplitude-shape method which takes into account the particular structure of some evolution problems, especially those described by partial differential equations. The method consists in transforming the system so that only a few equations remain stiff, the majority of the equations are non-stiff. The system is treated with a mixed explicit-implicit scheme which leads to a considerable reduction of numerical effort. We compare our approach with a classical solver of ordinary differential equations taking as an example, stiff systems of equations describing spatially dependent chemical kinetics.