Comparison of Solution Methods for the Boundary Function Equation

Abstract

We consider a second-order differential equation that describes the behavior of the "boundary function" -the zeroth-order boundary function of the asymptotic boundary function method. The dual operator formalism is applied to this equation. The result is an approximate solution of the problem that satisfies the boundary conditions on both boundaries. The boundary function obtained in this way is compared with the results of numerical solution of the exact differential equation.