  Recently a splitting approach has been presented for the simulation of
sonic-boom propagation. Splitting methods allow one to divide complicated
partial differential equations into simpler parts that are solved by
specifically tailored numerical schemes. The present work proposes a second
order exponential integrator for the numerical solution of sonic-boom
propagation modelled through a dispersive equation with Burgers' nonlinearity.
The linear terms are efficiently solved in frequency space through FFT, while
the nonlinear terms are efficiently solved by a WENO scheme. The numerical
method is designed to be highly parallelisable and therefore takes full
advantage of modern computer hardware. The new approach also improves the
accuracy compared to the splitting method and it reduces oscillations. The
enclosed numerical results illustrate that parallelisation on a CPU results in
a speedup of 22 times faster than the straightforward sequential version. The
GPU implementation further accelerates the runtime by a factor 3, which
improves to 5 when single precision is used instead of double precision.
