In this work, a number of numerical schemes are presented in the context of virtual-analog simulation. The schemes are linearlyimplicit 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.

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This paper presents an application of the port Hamiltonian formalism to the nonlinear simulation of the OTA-based Korg35 filter circuit and the Moog 4-pole ladder filter circuit. Lyapunov analysis is used with their state-space representations to guarantee zero-input stability over the range of parameters consistent with the actual circuits. A zero-input stable non-iterative discrete-time scheme based on a discrete gradient and a change of state variables is shown along with numerical simulations. Simulations show behavior consistent with the actual operation of the circuits, e.g., self-oscillation, and are found to be stable and have lower computational cost compared to iterative methods.

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For physical modelling sound synthesis, many techniques are available; time-stepping methods (e.g., finite-difference time-domain (FDTD) methods) have an advantage of flexibility and generality in terms of the type of systems they can model. These methods do, however, lack the capability of easily handling smooth parameter changes while retaining optimal simulation quality and stability, something other techniques are better suited for. In this paper, we propose an efficient method to smoothly add and remove grid points from a FDTD simulation under sub-audio rate parameter variations. This allows for dynamic parameter changes in physical models of musical instruments. An instrument such as the trombone can now be modelled using FDTD methods, as well as physically impossible instruments where parameters such as e.g. material density or its geometry can be made time-varying. Results show that the method does not produce (visible) artifacts and stability analysis is ongoing.

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In this paper, a complete simulation of a trombone using finitedifference time-domain (FDTD) methods is proposed. In particular, we propose the use of a novel method to dynamically vary the number of grid points associated to the FDTD method, to simulate the fact that the physical dimension of the trombone’s resonator dynamically varies over time. We describe the different elements of the model and present the results of a real-time simulation.

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