Approximate solutions for Non-Linear autonomous ODEs on the basis of PWL approximation theory

GARCIA, A., S. BIAGIOLA, L. CASTRO, J. L. FIGUEROA AND O. AGAMENNONI

Iasi, Rumania

Conferencia; International Conference on Applied Analysis and Differential Equations; 2006

Faculty of Mathematics, University "Al. I. Cuza" of Iasi and Institute "Octav Mayer" of the Romanian Academy

The present work introduces a new approach to the problem of describing the dynamic behavior of nonlinear autonomous systems. A general method to approximate the solutions of a set of ODEs is presented. The technique makes use of a PWL approximation of the ODEs vector field which describes the dynamics of a system. A measure of the dynamics approximation error is used to estimate upper and lower bounds for the error between the real and the approximate trajectories (i.e. the real and approximate solutions to the ODE). The proposed solution approach can be used in many applications. For instance, in the field of physical and (bio) chemical processes that exhibit nonlinear behavior. These ones, are good examples since many of them are modelled by systems of ODEs in continuous-time domain. Moreover, it could be used in the solution of dynamic optimization problems with significant advantages as regards computational time consumption. It is important to remark the possibility of the implementation of an integrated circuit capable to emulate PWL functions, thus providing a very efficient real time application.