Efficient solution of nonlinear models expressed in S-system canonical form

Abstract

The S-system is emerging as a general canonical form for analysis of nonlinear models. Models expressed within this regularly structured system of nonlinear ordinary differential equations are obtained by applying either of two different strategies: (A) Direct derivation of an S-system utilizing the Power Law Formalism; or (B) exact recasting of an existing, well established model into S-system form. By capitalizing on the regular structure of S-systems, efficient formulas for numerical solution of this general class have been developed. For any S-system it can be shown that these formulas are more efficient than conventional multistep formulas of the same order. For implemented methods, the actual improvements in efficiency are considerably more than the minimum estimates. Preliminary tests show that time required for solution of S-systems is reduced by one or two orders of magnitude -- the relative improvement in efficiency increases with size and complexity of the problem, and with degree of accuracy required.