Solving stiff system by Taylor series (Q1263946)

A new insight into the numerical solution of stiff systems of ODE's is brought by application of long Taylor series (up to 30 terms). Most of stiff problems are of the type where there is a linear ODE hidden within the stiff system of ODE's. When the hidden linear ODE is of order one, there is an exponential component in the solution. This exponential forces the integration stepsize to be very small in relation to the domain of the stiff problems. This exponential component is readily made appearent by an analysis of the Taylor series of the solution. A stiff problem from chemistry is analyzed in detail. Portions of the equations giving rise to stiffness are identified. It comes out that there are more than one hidden ODE. For analyzing problems of this complexity artificial stiff problems with up to stiff-order four are created by combining linear ODE's with a non-linear problem with known solutions. The Taylor series algorithm for solving stiff problems is implemented as an integral part of the ATOMFT system for the automatic solution of ODE's.