The theory and numerical computation of Maliuzhinets' special function

Abstract

Extension of the Institute's RCS code SIGMA to treat non-metallic wedges is based on a solution of corresponding diffraction problem given by G. D. Maliuzhinets. To compute this solution, a special function is needed which bears the name of Maliuzhinets. Evaluation of this function is rather time-consuming. One may try, however, to simplify the problem by developing approximations to the function, the accuracy of which is sufficient for practical RCS computations with SIGMA. This report presents a systematic analysis of the Maliuzhinets' special function. Complete theory of the function and its logarithmic derivative is given in chapter 2 of the report. We subsequently derive all known representations of the functions as well as prove various functional relations satisfied by them. Chapter 3 is devoted to construction of effective numerical algorithms for computing the Maliuzhinets' function. We analyze various representations of the function, their numerical advantages and disadvantages. Five various numerical schemes are proposed that differ from each other in accuracy and computational speed. Each scheme has been implemented in a FORTRAN subroutine and chapter 4 provides their detailed description, including program listings.