Order reduction in the integral equations of the null-field method

摘要

We reduce the system of equations of the null-field method in the problem of diffraction on a permeable scatterer to a single equation. For a special representation of the field inside the scatterer, we prove the equivalence of that equation to the original boundary value problem of diffraction. We state conditions of the convergence of the approximate solution to the exact one. We prove the completeness and closedness of a system of plane waves.