The nonlinear analytic nodal method, which is formulated by combining
the nonlinear iteration technique and the analytic nodal method (ANM),
requires analytic solutions of the two-node problems. When the method
is applied to problems that contain near-critical nodes in which ther
e is essentially no net leakage, the two-node ANM solution for such no
des results in highly ill-conditioned matrices and potential numerical
instabilities, especially in single precision arithmetic. Two stabili
zation techniques are introduced to resolve the instability problem by
employing alternate basis functions for near-critical nodes. The firs
t uses the exact ANM solution for a critical node, and the second empl
oys the nodal expansion method. Both techniques are shown to perform w
ell; however the solution accuracy can be mildly sensitive to the crit
erion used to invoke the stabilized coupling kernel.