A new wave description for nonlinear elements

A very important property of every numerical method is to calculate a solution with guarantee of stability and accuracy. The simulation of nonlinear systems gains nowadays in importance because modern computer generations allow the numerical solution of complex systems in an acceptable computer time. If wave digital (WD) filter principles are used to find a digital counterpart of a linear and passive system, we can guarantee that the WD algorithm is stable, i.e., the unavoidable errors caused by the discretisation in time and the quantization of signals do not change the properties of the system in an inadmissible manner. The WD method can be applied to nonlinear systems as well. But there always occur implicit equations by modeling nonlinear capacitances or inductances. In this paper, a new formulation is described to find a WD structure of these nonlinear elements without implicit equations in many cases. Therefore it is necessary to define new waves which have to be adopted to every kind of nonlinear element. The WD properties of the linear part of the system and the separated handling of each element are not affected by the new formulation. The mathematical pendulum will be modeled and simulated