On one method of solving the Helmholtz equation. I

Journal of Mathematical Physics

Volumn 22, Issue 1, 1981, Pages 32-38

  Verbitskii, I L ^a  

^a A USIKOV INSTITUTE OF RADIO PHYSICS AND ELECTRONICS   (Ukraine)

Author keywords

ALGORITHMS; ANALYTICAL SOLUTION; BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; DIFFRACTION; POISSON EQUATION

Indexed keywords

EID: 77958564941     PISSN: 00222488     EISSN: 10897658     Source Type: Journal    
DOI: 10.1063/1.524751     Document Type: Article

References (21)

1. Computer Techniques for Electromagnetics, edited by R. Mittra, International Series of Monographs in Electrical Engineering (Pergamon, Oxford, 1973), Vol7.
2. L. A. Weinstein, Diffraction Theory and Factorization Method (in Russian) (Soviet Radio, Moscow) 1966.
3. V. P. Shestopalov, “A method for the Riemann‐Hilbert Problem in Diffraction Theory and Electromagnetic Wave Propagation” (in Russian), Izdanja Khar’kov University, 1971.
4. I. L. Verbitskii, “Modern State of Slow‐Wave System Theory” (in Russian), a report at the VI All‐Union Seminar on oscillation phenomena in charged particle flows, Severo‐zapadnyi Zaochnyi Politeknicheskyi Institut, Leningrad, 1978.
5. I. L. Verbitskii, Dokl. Akad. Nauk SSSR 216, 1022 (1974).
6. I. L. Verbitskii, and N. Z. Remez, Dokl. Akad. Nauk SSSR 233, 323 (1977).
7. B. A. Samokish, Vestn. Leningr. Univ. Ser. Mat. Mekh. Astron. 160 (1964).
8. S. G. Mikhlin, Numerical Realization of Variational Methods (in Russian) (Nauka, Moscow) 1966.
9. H. Hönl, A.W. Maue, and K. Westpfahl, Theorie der Beugung. Handbuch der Physik, edited by S. Flügge (Springer, Berlin, 1961), Vol. 25, p. 218.
10. L. Bers, F. John, and M. Schechter, Partial Differentiai Equations (Interscience, New York) 1964.
11. N. A. Lavrentiev and B. V. Shabat, Methods of Theory of Complex Variable Functions (in Russian) (Gostekhizdat, Moscow) 1951.
12. S. E. Warschawski, Trans. Am. Math. Soc. 51, 280 (1942).
13. N. S. Koshliakov, E. B. GHner, and M. M. Smirnov, Basic Differential Equations of Mathematical Physics (in Russian) (Phizmatgiz, Moscow) 1962.
14. L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis (in Russian) (Phizmatgiz, Moscow) 1962.
15. L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces (in Russian) (Phizmatgiz, Moscow) 1959.
16. L. A. Weinstein, Zh. Tekh. Fiz. 27, 2109 (1957).
17. N. P. Zapol’nov, Some Questions of Calculating Electromagnetic Field in Slow‐Wave Systems (in Russian) (Soviet Radio, Moscow) 1973.
18. R. N. Hill, R. E. Kleinman, and E. W. Pfaff, Can. J. Phys. 51, 1541 (1973).
19. M. Neviere, M. Cadilhac, and R. Petit, IEEE Trans. Antennas Propag. 21, 37 (1973).
20. I. L. Verbitskii, Radiotekh. Elektron. 21, 485 (1976).
21. I. V. Verbitskii, IEEE Trans. Microwave Theory Tech. 28 (1) (1980).