Direct solution of nonlinear differential equations derived from real circuit applications

Abstract

The numeric solutions to nonlinear differential equations play a great role in many areas of engineering. In many cases all that is desired an accurate solution to a few points which can be calculated in a short time period. This study provides an exact solution to nonlinear ordinary differential equations arising from electrical circuit representation. This achievement is due to the application of the generalized trial equation. The exact solution gives a good analytic solution to a nonlinear equation that describes the action of a nonlinear electrical circuit. It is suggested that the methodology used herein may be useful in the study of other nonlinear problems described by differential equations approximated by an appropriate solution. In particular, the exact solution may be applied to the study of the cubic nonlinear circuit and system applications to prevent the difficulties that may arise due to approximation methods. The newly generated method that produces an exact solution tested for a pendulum, Poisson–Boltzmann, Duffing like electrical circuit applications.