  We develop a numerical method for the Westervelt equation, an important
equation in nonlinear acoustics, in the form where the attenuation is
represented by a class of non-local in time operators. A semi-discretisation in
time based on the trapezoidal rule and A-stable convolution quadrature is
stated and analysed. Existence and regularity analysis of the continuous
equations informs the stability and error analysis of the semi-discrete system.
The error analysis includes the consideration of the singularity at $t = 0$
which is addressed by the use of a correction in the numerical scheme.
Extensive numerical experiments confirm the theory.
