A CONVERGENT METHOD FOR SOLVING THE BALANCE EQUATION

Abstract

The nonlinear balance equation is replaced by an infinite system of linear differential equations. This system has a series of solutions which under certain conditions converge toward the solution of the balance equation. It is shown that these conditions coincide with the conditions for ellipticity of the balance equation. A slightly different method of solution is shown to diverge. This is illustrated by a case where the sequence of approximate solutions is compared with the solution of the balance equation.