Revisiting the Second-Order Accurate Non-Iterative Discretization Scheme
In the field of virtual analog modeling, a variety of methods have been proposed to systematically derive simulation models from circuit schematics. However, they typically rely on implicit numerical methods to transform the differential equations governing the circuit to difference equations suitable for simulation. For circuits with non-linear elements, this usually means that a non-linear equation has to be solved at run-time at high computational cost. As an alternative to fully-implicit numerical methods, a family of non-iterative discretization schemes has recently been proposed, allowing a significant reduction of the computational load. However, in the original presentation, several assumptions are made regarding the structure of the ODE, limiting the generality of these schemes. Here, we show that for the second-order accurate variant in particular, the method is applicable to general ODEs. Furthermore, we point out an interesting connection to the implicit midpoint method.