A convergence analysis of a numerical method for solving the balance equation

In this report the convergence of an iterative method for solving the nonlinear balance equation is analyzed. It is shown that this iterative method will be convergent if a sufficiently accurate initial approximation is used and if the subsequent iterates satisfy the ellipticity condition.
Otherwise if the successive approximate solutions do not all satisfy the ellipticity condition the method may be divergent. We shall describe what can be done to make the method convergent in this case. Experimental results are given.