has characteristic modelling and simulation algorithm deterministic system behaviour progression with adaptive time step approximate solution S-System power-law canonical differential equations solver 2011-05-20 http://identifiers.org/biosimulators/ecell4 http://identifiers.org/doi/10.1137/0727042 AZ ESSYNS GMA Ordinary differential equations can be recast into a nonlinear canonical form called an S-system. Evidence for the generality of this class comes from extensive empirical examples that have been recast and from the discovery that sets of differential equations and functions, recognized as among the most general, are special cases of S-systems. Identification of this nonlinear canonical form suggests a radically different approach to numerical solution of ordinary differential equations. By capitalizing on the regular structure of S-systems, efficient formulas for a variable-order, variable-step Taylor-series method are developed. ordinary differential equation problem