  The leading order Green's function solutions of the general relativistic thin
disc equations are computed, using a pseudo-Newtonian potential and asymptotic
Laplace mode matching techniques. This solution, valid for a vanishing ISCO
stress, is constructed by ensuring that it reproduces the leading order
asymptotic behaviour of the near-ISCO, Newtonian, and global WKB limits.
Despite the simplifications used in constructing this solution, it is typically
accurate, for all values of the Kerr spin parameter $a$ and at all radii, to
less than a percent of the full numerically calculated solutions of the general
relativistic disc equations. These solutions will be of use in studying
time-dependent accretion discs surrounding Kerr black holes.
