In this book, relatively simple difference strategies will be employed whenever possible. On the other hand, sometimes more accurate methods are necessary, especially when one is interested in more delicate modeling of musical instrument physics. There is a large variety of time differencing methods which are in use for the solutions of ODEs; normally, these are framed in terms of a first-order system, and so do not fit well into the main development here. Some of the better known are Adams-Bashforth, Adams-Moulton and Runge-Kutta methods, and will be discussed in the context of spectral methods in §13.5.