Non-Iterative Simulation Methods for Virtual Analog Modelling

The simulation of nonlinear components is central to virtual analog simulation. In audio effects, circuit elements often include devices such as diodes and transistors, mostly operating in the strongly regime. Mathematical models are form systems ordinary differential equations (ODEs), traditional integrators, trapezoid midpoint methods, can be employed solvers. These methods fully implicit, require solution a algebraic system at each time step, introducing further complications regarding existence uniqueness solution, well choice halting conditions for iterative root finder. On other hand, fast explicit Forward Euler, or Runge-Kutta prone unstable behaviour standard sample rates, even moderate amplitudes. For these reasons, this work family linearly-implicit schemes presented. take perturbation expansion, making construction higher-order possible. Compared with classic implicit designs, proposed have advantage efficiency, since update computed single iteration, through linear equations. Furthermore, proven by simple inspection matrix. display stable rates. case scalar ODE, sufficient numerical stability derived, imposing constraints on sampling rate. Several theoretical results provided, examples typical stiff used modelling.