Amplitude-shape method for the numerical solution of ordinary differential equations.

Abstract

In this work, we present an amplitude-shape method for solving evolution problems described

by partial differential equations. The method is capable of recognizing the special

structure of many evolution problems. In particular, the stiff system of ordinary differential

equations resulting from the semi-discretization of partial differential equations is considered.

The method involves transforming the system so that only a few equations are stiff

and the majority of the equations remain non-stiff. The system is treated with a mixed

explicit-implicit scheme with a built-in error control mechanism. This approach proved to

be very effective for the solution of stiff systems of equations describing spatially dependent

chemical kinetics.