In 'supersingular' scattering the potential $g^2U_A(r)$ involves a variable
nonlinear parameter $A$ upon the increase of which the potential also increases
beyond all limits everywhere off the origin and develops a uniquely high level
of singularity in the origin. The problem of singular scattering is shown here
to be solvable by iteration in terms of a smooth version of the semiclassical
approach to quantum mechanics. Smoothness is achieved by working with a pair of
centrifugal strengths within each channel. In both of the exponential and
trigonometric regions, integral equations are set up the solutions of which
when matched smoothly may recover the exact scattering wave function. The
conditions for convergence of the iterations involved are derived for both
fixed and increasing parameters. In getting regular scattering solutions, the
proposed procedure is, in fact, supplementary to the Born series by widening
its scope and extending applicability from nonsingular to singular potentials
and from fixed to asymptotically increasing, linear and nonlinear, dynamical
parameters.