  A numerical scheme is presented for the solution of Fredholm second-kind
boundary integral equations with right-hand sides that are singular at a finite
set of boundary points. The boundaries themselves may be non-smooth. The
scheme, which builds on recursively compressed inverse preconditioning (RCIP),
is universal as it is independent of the nature of the singularities. Strong
right-hand-side singularities, such as $1/|r|^\alpha$ with $\alpha$ close to
$1$, can be treated in full machine precision. Adaptive refinement is used only
in the recursive construction of the preconditioner, leading to an optimal
number of discretization points and superior stability in the solve phase. The
performance of the scheme is illustrated via several numerical examples,
including an application to an integral equation derived from the linearized
BGKW kinetic equation for the steady Couette flow.
