  This paper presents a simple and effective new numerical scheme for the
computation of electrostatic fields exterior to a collection of
close-to-touching discs. The method is presented in detail for the two-cylinder
case. The key idea is to represent the required complex potential using a
hybrid set of basis functions comprising the usual Fourier-Laurent expansion
about each circle centre comple- mented by a subsidiary expansion in a variable
associated with conformal mapping of the physical domain to a concentric
annulus domain. We also rigorously prove that there is a representation of the
solution in the hybrid basis with faster decay rate of coefficients than is
obtained by using a non-hybrid basis, thereby providing a rationalization for
the success of the method. The numerical scheme is easy to implement and
adaptable to the case of multiple close-to-touching cylinders.
