Analytical Regularization Method for bodies and screens of revolution with Neumann boundary conditions

A detailed explanation of a mathematically rigorous method for numerical simulation of scalar wave diffraction by bodies and infinitely thin screens of revolution is given. The method reduces the diffraction problem to an equivalent system of equations of the second kind that permits numerical solution to be obtained with any predetermined accuracy. The method employs an accumulated set of techniques of the Analytical Regularization Method. The set involves a “contour closing procedure”, proper scaling of the kernel of the corresponding differential-integral equation, Abel integral transforms, techniques of Dual Series Equation involving Jacoby polynomials and Legendre functions, and related ideas.