Non-Iterative Schemes for the Simulation of Nonlinear Audio Circuits

Abstract

In this work, a number of numerical schemes are presented in the context of virtual-analog simulation. The schemes are linearly-implicit in character, and hence directly solvable without iterative methods. Schemes of increasing order of accuracy are constructed, and convergence and stability conditions are proven formally. The schemes are able to handle stiff problems very efficiently, because of their fast update, and can be run at higher sample rates to reduce aliasing. The cases of the diode clipper and ring modulator are investigated in detail, including several numerical examples.