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

摘要

In the last few decades many types of nonlinear components that operate in switching modes have appeared in electrical and electronics engineering. Exact modeling of systems containing such components usually leads to sophisticated differential equations of which analytic solutions can hardly be found, or cannot be computed in many cases. On the other hand, the numerical solutions involve computational errors either due to the wide-spread time constants or very small damping ratios which usually lead to overcontinuing oscillations. 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.