Approximate Solutions for Non-linear Autonomous ODEs on the Basis of PWL Approximation Theory

GARCIA, A.G.; BIAGIOLA, S.I.; FIGUEROA, J.L.; AGAMENNONI, O.E.; CASTRO, L.R.

Applied Analysis and Differential Equations

World Scientific

Lugar: Singapur; Año: 2007; p. 113 - 126

In this paper the general approach to approximate the solutions of Ordinary Differential Equations (ODEs) is presented. The methodology uses a Piecewise Linear (PWL) approximation of the ODEs vector field which describes the dynamics of a system. Once the number of Simplices to include in the PWL approximation of the nonlinear vector field has been decided, a measure of the dynamics approximation error is used to estimate upper and lower bounds for the error between the actual and approximated trajectories. Several examples are analyzed to illustrate the method. A comparison with a classical numerical solution is provided to show some advantages of the proposed technique.