  Occurring in protoplanetary discs composed of dust and gas, streaming
instabilities are a favoured mechanism to drive the formation of planetesimals.
The Polydispserse Streaming Instability is a generalisation of the Streaming
Instability to a continuum of dust sizes. This second paper in the series
provides a more in-depth derivation of the governing equations and presents
novel numerical methods for solving the associated linear stability problem. In
addition to the direct discretisation of the eigenproblem at second order
introduced in the previous paper, a new technique based on numerically reducing
the system of integral equations to a complex polynomial combined with root
finding is found to yield accurate results at much lower computational cost. A
related method for counting roots of the dispersion relation inside a contour
without locating those roots is also demonstrated. Applications of these
methods show they can reproduce and exceed the accuracy of previous results in
the literature, and new benchmark results are provided. Implementations of the
methods described are made available in an accompanying Python package
psitools.
