Event-based generation of approximate solutions of nonlinear differential equations

This paper investigates the error between the approximate and exact solutions of a class of nonlinear differential equations which possess unique solution on a certain interval for any admissible initial conditions. The differential equations are assumed to be approximated by well-posed truncated Taylor series up to a certain order obtained about certain, in general non-periodic, sampling points t_i ϵ [t₀, t_J] for i = 0,1,..., J of the solution. Two simulation examples are also provided. The first one is concerned with a predefined periodic sampling law while the second one generates new sampling points according to a constant amplitude difference sampling criterion.