Recursive procedures for plotting the profile curves and estimating the stability of capillary shaping processes

A method is proposed whereby specially selected integrable comparison equations are used to obtain a solution to Laplace's capillary equations. The comparison equations, used together with certain recursive procedures, make it possible to solve the initial equation with any desired accuracy. Lower- and upper-bound approximations of the solution to the capillary equation are presented. The plotting of profile curves is illustrated by an example for the case of Stepanov growth; the stability of capillary shaping processes is analyzed.