Comparison of methods for solving the diffraction problem for a step in a waveguide

✍ Scribed by G.V. Voskresenskii; E.A. Galst'yan; S.M. Zhurav

• Book ID: 104263313
• Publisher: Elsevier Science
• Year: 1983
• Weight: 374 KB
• Volume: 23
• Category: Article
• ISSN: 0041-5553
• DOI: 10.1016/s0041-5553(83)80176-1

✦ Synopsis

From ( 19) and ( 22) we have F(x,O)=A1(x)-tN(x), -L<x<L, (

Let us now study the behaviour of the functions f(z) and F(.) at the ends (-L, 0), (L, 0). From ( 15) and ( 16), using the expressions for the behaviour of a Cauchy integral close to the ends of the line of integration in class H' of functions /5/, we have, as .~(-L, m f(z) .... Ci, F(.) .... M(-L), ( 24) and as ..... (L, 0) f(.) .... Ci, F(.) .... M(L), (25) Finally, substituting expressions ( 15) and ( 16) into (6) and using (23)--( 25), ( 18), we obtain the solution of our problem, satisfying conditions (2).

A similar problem was considered for the semi-infinite case in /7--9/.