Ordinary differential equations with strong nonlinearities and their numerical solutions with abrupt changes

In the last few decades many types of nonlinear components that operate in switching modes have appeared in electrical and electronics engineering. Ex act modeling of systems containing such components usually Leads to sophist icated differential equations of which analytic solutions can hardly be fou nd, or cannot be computed in many cases. On the other hand, the numerical s olutions involve computational errors either due to the wide-spread time co nstants or very small damping ratios which usually lead to overcontinuing o scillations. This paper is aimed to show the ease in treating the switching type strong nonlinearities by using piecewise linearization in conjunction with the switching equations evaluating the discontinuities. (C) 2001 Else vier Science Inc, All rights reserved.