We evaluate longitudinal resistive wakefields for cylindrical beam pipes
numerically and compare the results with existing approximate formul\ae. We
consider an ultra-relativistic bunch traversing a cylindrical, metallic tube
for a model in which the wall conductivity is taken to be first independent and
second dependent on frequency, and we show how these can be included simply and
efficiently in particle tracking simulations. We also extend this to higher
order modes, and to the transverse wakes. This full treatment can be necessary
in the design of modern nano-beam accelerators
